BSPL Toolbox

Bézier toolbox for advanced curve analysis and processing, optimised for accuracy and speed.

BSPL

Bézier curve evaluation. https://uk.mathworks.com/matlabcentral/fileexchange/109179-high-precision-bezier-curves

x = rand(4, 2);
b = bspl(x);
b = bspl(x, 50);
b = bspl(x, rand(3, 1));
b = bspl(x, [], 1);
b = bspl(x, 1e3, 2, [1, 3, 3, 1]);

BSPLARC

Bézier curve arc-length calculation or estimation.

x = rand(4, 2);
a = bsplarc(x);
a = bsplarc(x, [0 0.5]);
a = bsplarc(x, [], 1);
a = bsplarc(x, 100, -1);

BPSLBOX

Bézier curve bounding box or tight bounding box.

x = rand(4, 3);
y = bsplbox(x);
y = bsplbox(x, 1);
y = bsplbox(x, [], 0);

BSPLC1D

Bézier curve discrete 1D curvature and normals.

x = bspl(rand(4, 3));
[k, n] = bsplc1d(x);
k = bsplc1d(x, []);

BSPLCRV

Bézier analytic signed curvature.

x = rand(4, 2);
k = bsplcrv(x);
k = bsplcrv(x, 100);

BSPLCSP

Bézier calculation of cusps and inflections (convexity).

x = rand(4, 2);
[y, t, z] = bsplcsp(x);
y = bsplcsp(x, []);
y = bsplcsp(x, 1);

BSPLCUT

Bézier curve subdivision.

x = rand(4, 2);
y = bsplcut(x);
y = bsplcut(x, rand(2, 1));
y = bsplcut(x, 3);

BSPLDCJ

Bézier curve evaluation using De-Casteljau.

x = rand(4, 2);
b = bspldcj(x); 
b = bspldcj(x, 20);
b = bspldcj(x, rand(50, 1));

BSPLDER

Bézier curve derivatives or hodograph.

x = rand(5, 2);
y = bsplder(x, 3);

BSPLDIS

Bézier curve with uniform sampling.

x = rand(4, 3);
y = bspldis(x);
[y, t] = bspldis(x, 5); 

BSPLFIT

Bézier curve fitting.

x = rand(5, 2);
[y, res, t] = bsplfit(x);
y = bsplfit(x, 3);
y = bsplfit(x, [], 0);
y = bsplfit(x, 3, 1);
y = bsplfit(x, [], 1e2);

BSPLFUN

Bézier curve algebraic operations.

x = rand(5, 3);
y = rand(4, 3);
z = bsplfun(x, y, 'plus');
z = bsplfun(x, x, -y, '*');
z = bsplfun(x, y, 'cross');

BSPLGET

Bézier curve control point finder.

x = rand(4, 2);
y = bsplget(x);
y = bsplget(x, 0);
y = bsplget(x, 1);
y = bsplget(x, 1e4);

BSPLINT

Bézier curve intersections or self-intersections.

x = rand(5, 2);
y = rand(4, 2);
[t, y] = bsplint(x, y);
t = bsplint(x);
t = bsplint(x, 0.5);

BSPLKIN

Bézier curve knot insertion.

x = rand(5, 2);
y = bsplkin(x, 3);

BSPLPCW

Bézier curve piecewise or composite construction (open or closed).

x = rand(4, 2);
y = bsplpcw(x);
y = bsplpcw(x, []);

BSPLPRO

Bézier curve point projection.

x = rand(4, 2);
y = rand(2, 2);
z = bsplpro(x, y); 

BSPLVEC

Bézier curve tangent and normals.

x = rand(4, 2);
[t, n] = bsplvec(x);
t = bsplvec(x, 100);
t = bsplvec(x, rand(4, 1));
t = bsplvec(x, [], 1);

BER2BEZ

Polynomial to Bézier coefficients.

x = rand(4, 2);
y = ber2bez(x); 

BEZ2BER

Bézier to polynomial coefficients.

x = rand(4, 2);
y = bez2ber(x);