sbplib: +grid/Curve.m annotate

annotate +grid/Curve.m @ 103:bc5db54f9efd feature/arclen-param

fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.

author	Martin Almquist <martin.almquist@it.uu.se>
date	Mon, 07 Dec 2015 17:24:28 +0100
parents	ecf77a50d4fe
children	ffd9e68f63cc

rev	line source
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	1 classdef Curve
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	2 properties
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	3 g
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	4 gp
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	5 transformation
87 0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that). Martin Almquist <martin.almquist@it.uu.se> parents: 86 diff changeset	6
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	7 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	8 methods
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	9 %TODO:
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	10 % Errors or FD if there is no derivative function added.
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	11 % -semi-done
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	12
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	13 % Concatenation of curves
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	14 % Subsections of curves
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	15 % Stretching of curve parameter - semi-done
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	16 % Curve to cell array of linesegments
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	17
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	18 % The curve parameter t must be in [0,1].
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	19 % Can supply derivative.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	20 function obj = Curve(g,gp,transformation)
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	21 default_arg('gp',[]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	22 default_arg('transformation',[]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	23 p_test = g(0);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	24 assert(all(size(p_test) == [2,1]), 'A curve parametrization must return a 2x1 vector.');
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	25
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	26 if ~isempty(transformation)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	27 transformation.base_g = g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	28 transformation.base_gp = gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	29 [g,gp] = grid.Curve.transform_g(g,gp,transformation);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	30 end
87 0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that). Martin Almquist <martin.almquist@it.uu.se> parents: 86 diff changeset	31
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	32 obj.g = g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	33 obj.gp = gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	34 obj.transformation = transformation;
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	35
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	36 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	37
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	38 function n = normal(obj,t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	39 deriv = obj.gp(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	40 normalization = sqrt(sum(deriv.^2,1));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	41 n = [-deriv(2,:)./normalization; deriv(1,:)./normalization];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	42 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	43
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	44
87 0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that). Martin Almquist <martin.almquist@it.uu.se> parents: 86 diff changeset	45 % Plots a curve g(t) for 0<t<1, using n points. Returns a handle h to the plotted curve.
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	46 % h = plot_curve(g,n)
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	47 function h = plot(obj,n)
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	48 default_arg('n',100);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	49
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	50 t = linspace(0,1,n);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	51 p = obj.g(t);
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	52 h = line(p(1,:),p(2,:));
87 0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that). Martin Almquist <martin.almquist@it.uu.se> parents: 86 diff changeset	53 end
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	54
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	55 function h= plot_normals(obj,l,n,m)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	56 default_arg('l',0.1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	57 default_arg('n',10);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	58 default_arg('m',100);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	59 t_n = linspace(0,1,n);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	60
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	61 normals = obj.normal(t_n)*l;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	62
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	63 n0 = obj.g(t_n);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	64 n1 = n0 + normals;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	65
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	66 h = line([n0(1,:); n1(1,:)],[n0(2,:); n1(2,:)]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	67 set(h,'Color',Color.red);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	68 obj.plot(m);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	69 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	70
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	71 function h= show(obj,name)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	72 p = obj.g(1/2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	73 n = obj.normal(1/2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	74 p = p + n*0.1;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	75
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	76 % Add arrow
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	77
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	78 h = text(p(1),p(2),name);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	79 h.HorizontalAlignment = 'center';
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	80 h.VerticalAlignment = 'middle';
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	81
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	82 obj.plot();
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	83 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	84 % Shows curve with name and arrow for direction.
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	85
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	86 % Length of arc from parameter t0 to t1 (which may be vectors).
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	87 % Computed using derivative.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	88 function L = arcLength(obj,t0,t1)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	89 assert(~isempty(obj.gp),'Curve has no derivative!');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	90 speed = @(t) sqrt(sum(obj.gp(t).^2,1));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	91 L = integral_vec(speed,t0,t1);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	92 end
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	93
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	94 % Arc length parameterization.
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	95 function curve = arcLengthParametrization(obj,N)
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	96 default_arg('N',100);
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	97
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	98 % Construct arcLength function using splines
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	99 tvec = linspace(0,1,N);
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	100 arcVec = obj.arcLength(0,tvec);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	101 arcLength = spline(tvec,arcVec);
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	102
99 ecf77a50d4fe The arclength parameter function was slow because it called fzero. Now it is constructed once and for all with splines. Much better performance. Martin Almquist <martin.almquist@it.uu.se> parents: 98 diff changeset	103 % Stretch the parameter, construct function with splines
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	104 arcParVec = fzero_vec(@(s)arcLength(s) - tvecarcLength(1),[0-10eps,1+10*eps]);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	105 arcPar = spline(tvec,arcParVec);
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	106
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	107 % New function and derivative
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	108 g_new = @(t)obj.g(arcPar(t));
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	109 gp_new = @(t) normalize(obj.gp(arcPar(t)));
98 b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	110 curve = grid.Curve(g_new,gp_new);
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow. Martin Almquist <martin.almquist@it.uu.se> parents: 87 diff changeset	111
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	112 end
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	113
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	114 % how to make it work for methods without returns
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	115 function p = subsref(obj,S)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	116 %Should i add error checking here?
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	117 %Maybe if you want performance you fetch obj.g and then use that
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	118 switch S(1).type
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	119 case '()'
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	120 p = obj.g(S.subs{1});
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	121 % case '.'
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	122
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	123 % p = obj.(S.subs);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	124 otherwise
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	125 p = builtin('subsref',obj,S);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	126 % error()
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	127 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	128 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	129
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	130
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	131 %% TRANSFORMATION OF A CURVE
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	132 function D = reverse(C)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	133 % g = C.g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	134 % gp = C.gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	135 % D = grid.Curve(@(t)g(1-t),@(t)-gp(1-t));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	136 D = C.transform([],[],-1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	137 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	138
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	139 function D = transform(C,A,b,flip)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	140 default_arg('A',[1 0; 0 1]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	141 default_arg('b',[0; 0]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	142 default_arg('flip',1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	143 if isempty(C.transformation)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	144 g = C.g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	145 gp = C.gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	146 transformation.A = A;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	147 transformation.b = b;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	148 transformation.flip = flip;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	149 else
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	150 g = C.transformation.base_g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	151 gp = C.transformation.base_gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	152 A_old = C.transformation.A;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	153 b_old = C.transformation.b;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	154 flip_old = C.transformation.flip;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	155
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	156 transformation.A = A*A_old;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	157 transformation.b = A*b_old + b;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	158 transformation.flip = flip*flip_old;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	159 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	160
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	161 D = grid.Curve(g,gp,transformation);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	162
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	163 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	164
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	165 function D = translate(C,a)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	166 g = C.g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	167 gp = C.gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	168
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	169 % function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	170 % x = g(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	171 % v(1,:) = x(1,:)+a(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	172 % v(2,:) = x(2,:)+a(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	173 % end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	174
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	175 % D = grid.Curve(@g_fun,gp);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	176
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	177 D = C.transform([],a);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	178 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	179
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	180 function D = mirror(C, a, b)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	181 assert_size(a,[2,1]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	182 assert_size(b,[2,1]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	183
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	184 g = C.g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	185 gp = C.gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	186
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	187 l = b-a;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	188 lx = l(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	189 ly = l(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	190
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	191
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	192 % fprintf('Singular?\n')
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	193
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	194 A = [lx^2-ly^2 2lxly; 2lxly ly^2-lx^2]/(l'*l);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	195
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	196 % function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	197 % % v = a + A*(g(t)-a)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	198 % x = g(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	199
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	200 % ax1 = x(1,:)-a(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	201 % ax2 = x(2,:)-a(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	202 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	203 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	204 % end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	205
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	206 % function v = gp_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	207 % v = A*gp(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	208 % end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	209
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	210 % D = grid.Curve(@g_fun,@gp_fun);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	211
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	212 % g = A(g-a)+a = Ag - Aa + a;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	213 b = - A*a + a;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	214 D = C.transform(A,b);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	215
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	216 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	217
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	218 function D = rotate(C,a,rad)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	219 assert_size(a, [2,1]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	220 assert_size(rad, [1,1]);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	221 g = C.g;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	222 gp = C.gp;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	223
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	224
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	225 A = [cos(rad) -sin(rad); sin(rad) cos(rad)];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	226
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	227 % function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	228 % % v = a + A*(g(t)-a)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	229 % x = g(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	230
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	231 % ax1 = x(1,:)-a(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	232 % ax2 = x(2,:)-a(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	233 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	234 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	235 % end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	236
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	237 % function v = gp_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	238 % v = A*gp(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	239 % end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	240
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	241 % D = grid.Curve(@g_fun,@gp_fun);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	242
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	243
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	244 % g = A(g-a)+a = Ag - Aa + a;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	245 b = - A*a + a;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	246 D = C.transform(A,b);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	247 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	248 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	249
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	250 methods (Static)
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	251
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	252 function gp_out = numerical_derivative(g,D1)
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	253 m = length(D1); L = 1; % Assume curve parameter from 0 to 1.
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	254 t = linspace(0,L,m);
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	255 gVec = g(t)';
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	256 gpVec = (D1*gVec)';
87 0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that). Martin Almquist <martin.almquist@it.uu.se> parents: 86 diff changeset	257
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	258 gp1_fun = spline(t,gpVec(1,:));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	259 gp2_fun = spline(t,gpVec(2,:));
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	260 gp_out = @(t) [gp1_fun(t);gp2_fun(t)];
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	261
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	262 end
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	263
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	264 function obj = line(p1, p2)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	265
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	266 function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	267 v(1,:) = p1(1) + t.*(p2(1)-p1(1));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	268 v(2,:) = p1(2) + t.*(p2(2)-p1(2));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	269 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	270 g = @g_fun;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	271
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	272 obj = grid.Curve(g);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	273 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	274
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	275 function obj = circle(c,r,phi)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	276 default_arg('phi',[0; 2*pi])
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	277 default_arg('c',[0; 0])
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	278 default_arg('r',1)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	279
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	280 function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	281 w = phi(1)+t*(phi(2)-phi(1));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	282 v(1,:) = c(1) + r*cos(w);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	283 v(2,:) = c(2) + r*sin(w);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	284 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	285
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	286 function v = g_fun_deriv(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	287 w = phi(1)+t*(phi(2)-phi(1));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	288 v(1,:) = -(phi(2)-phi(1))rsin(w);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	289 v(2,:) = (phi(2)-phi(1))rcos(w);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	290 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	291
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	292 obj = grid.Curve(@g_fun,@g_fun_deriv);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	293 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	294
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	295 function obj = bezier(p0, p1, p2, p3)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	296 function v = g_fun(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	297 v(1,:) = (1-t).^3p0(1) + 3(1-t).^2.tp1(1) + 3(1-t).t.^2p2(1) + t.^3p3(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	298 v(2,:) = (1-t).^3p0(2) + 3(1-t).^2.tp1(2) + 3(1-t).t.^2p2(2) + t.^3p3(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	299 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	300
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	301 function v = g_fun_deriv(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	302 v(1,:) = 3(1-t).^2(p1(1)-p0(1)) + 6(1-t).t(p2(1)-p1(1)) + 3t.^2*(p3(1)-p2(1));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	303 v(2,:) = 3(1-t).^2(p1(2)-p0(2)) + 6(1-t).t(p2(2)-p1(2)) + 3t.^2*(p3(2)-p2(2));
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	304 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	305
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	306 obj = grid.Curve(@g_fun,@g_fun_deriv);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	307 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	308
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	309
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	310 function [g_out,gp_out] = transform_g(g,gp,tr)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	311 A = tr.A;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	312 b = tr.b;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	313 flip = tr.flip;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	314
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	315 function v = g_fun_noflip(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	316 % v = A*g + b
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	317 x = g(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	318
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	319 v(1,:) = A(1,:)*x+b(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	320 v(2,:) = A(2,:)*x+b(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	321 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	322
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	323 function v = g_fun_flip(t)
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	324 % v = A*g + b
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	325 x = g(1-t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	326
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	327 v(1,:) = A(1,:)*x+b(1);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	328 v(2,:) = A(2,:)*x+b(2);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	329 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	330
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	331
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	332 switch flip
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	333 case 1
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	334 g_out = @g_fun_noflip;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	335 gp_out = @(t)A*gp(t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	336 case -1
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	337 g_out = @g_fun_flip;
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	338 gp_out = @(t)-A*gp(1-t);
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	339 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	340 end
48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	341
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	342 end
0 48b6fb693025 Initial commit. Jonatan Werpers <jonatan@werpers.com> parents: diff changeset	343 end
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	344
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	345 function g_norm = normalize(g0)
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	346 g1 = g0(1,:);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	347 g2 = g0(2,:);
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	348 normalization = sqrt(sum(g0.^2,1));
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	349 g_norm = [g1./normalization; g2./normalization];
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	350 end
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	351
103 bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	352 function I = integral_vec(f,a,b)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	353 % Wrapper around the built-in function integral that
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	354 % handles multiple limits.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	355
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	356 Na = length(a);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	357 Nb = length(b);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	358 assert(Na == 1 \|\| Nb == 1 \|\| Na==Nb,...
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	359 'a and b must have same length, unless one is a scalar.');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	360
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	361 if(Na>Nb);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	362 I = zeros(size(a));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	363 for i = 1:Na
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	364 I(i) = integral(f,a(i),b);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	365 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	366 elseif(Nb>Na)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	367 I = zeros(size(b));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	368 for i = 1:Nb
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	369 I(i) = integral(f,a,b(i));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	370 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	371 else
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	372 I = zeros(size(b));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	373 for i = 1:Nb
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	374 I(i) = integral(f,a(i),b(i));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	375 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	376 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	377 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	378
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	379 function I = fzero_vec(f,lim)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	380 % Wrapper around the built-in function fzero that
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	381 % handles multiple functions (vector-valued f).
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	382
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	383 fval = f(lim(1));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	384 I = zeros(size(fval));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	385
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	386 for i = 1:length(fval)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	387 e = zeros(size(fval));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	388 e(i) = 1;
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	389 I(i) = fzero(@(t) sum(e.*f(t)),lim);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	390 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	391
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	392 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	393
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	394 % Returns a function handle to the spline.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	395 function f = spline(tval,fval,spline_order)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	396 default_arg('spline_order',4);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	397 [m,~] = size(tval);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	398 assert(m==1,'Need row vectors.');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	399
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	400 % make vectors longer to be safe slightly beyond edges.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	401 dt0 = tval(2)-tval(1); dt1 = tval(end)-tval(end-1);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	402 df0 = fval(2)-fval(1); df1 = fval(end)-fval(end-1);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	403 tval = [tval(1)-dt0, tval, tval(end)+dt1];
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	404 fval = [fval(1)-df0, fval, fval(end)+df1];
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	405
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	406 f_spline = spapi( optknt(tval,spline_order), tval, fval );
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	407 f = @(t) fnval(f_spline,t);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	408 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore. Martin Almquist <martin.almquist@it.uu.se> parents: 99 diff changeset	409
86 3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	410
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments. Martin Almquist <martin.almquist@it.uu.se> parents: 0 diff changeset	411

Mercurial > repos > public > sbplib

annotate +grid/Curve.m @ 103:bc5db54f9efd feature/arclen-param