Other way or suggestion to build Bezier surface

Hi, My name Malina from Malaysia and i'm a student. I'm working with Bezier and B-spline modelling. I'm using Matlab 2018. My question is

(1)I having a problem to build Bezier surface because the function that u suggest in internet cannot found and do not exist in my matlab. For example Got error. Can you help to solve my problem with new suggestion that i can be use in my Matlab.

(2)My second question is can you give example some example of how to build B-spline curve because the guideline 'help' in Matlab dont have any example on B-spline curve like Bezier curve. I know the Bezier curve we can use Bernstein function. But B-spline do not have any example and some figure of B-spline curve.

Hope you can help me with this two question.

Answer 1

[Aditya]

Hi Malina,

1) Building a Bézier Surface in MATLAB:

If you don't have built-in functions for Bézier surfaces in your version of MATLAB, you can create a Bézier surface using the Bernstein polynomial basis. Here's a basic example of how to construct a Bézier surface:

% Define control points for a Bézier surface
controlPoints = zeros(4, 4, 3);  % Example with 4x4 control points in 3D

% Example control points (you should define these based on your specific surface)
controlPoints(:, :, 1) = [0 1 2 3; 0 1 2 3; 0 1 2 3; 0 1 2 3];  % X-coordinates
controlPoints(:, :, 2) = [0 0 0 0; 1 1 1 1; 2 2 2 2; 3 3 3 3];  % Y-coordinates
controlPoints(:, :, 3) = [0 1 0 1; 1 2 1 2; 0 1 0 1; 1 2 1 2];  % Z-coordinates

% Define parameters for Bézier surface
u = linspace(0, 1, 50);
v = linspace(0, 1, 50);
[U, V] = meshgrid(u, v);

% Initialize surface points
surfPoints = zeros(size(U, 1), size(V, 2), 3);

% Calculate Bézier surface points
for i = 1:4
    for j = 1:4
        B_ij = bernstein(i-1, 3, U) .* bernstein(j-1, 3, V);
        for k = 1:3
            surfPoints(:, :, k) = surfPoints(:, :, k) + B_ij .* controlPoints(i, j, k);
        end
    end
end

% Plot Bézier surface
surf(surfPoints(:, :, 1), surfPoints(:, :, 2), surfPoints(:, :, 3));
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Bézier Surface');

% Helper function for Bernstein polynomial
function B = bernstein(i, n, t)
    B = nchoosek(n, i) .* (t.^i) .* ((1-t).^(n-i));
end

2) Building a B-spline Curve in MATLAB

For B-spline curves, you can use the spapi function from the Spline Toolbox for constructing a spline interpolant. Here's a simple example:

% Define knot vector and control points
knots = [0 0 0 1 2 3 4 4 4];  % Example knot vector for cubic B-spline
controlPoints = [0 1 2 3 4; 0 1 0 1 0];  % Control points (2D example)

% Create B-spline using spapi
degree = 3;  % Degree of the B-spline
bSpline = spapi(knots, controlPoints);

% Evaluate B-spline curve
t = linspace(0, 4, 100);  % Parameter values
curvePoints = fnval(bSpline, t);

% Plot B-spline curve
plot(curvePoints(1, :), curvePoints(2, :), 'b-', 'LineWidth', 2);
hold on;
plot(controlPoints(1, :), controlPoints(2, :), 'ro--');  % Control polygon
xlabel('X');
ylabel('Y');
title('B-spline Curve');
legend('B-spline Curve', 'Control Polygon');