I need a program with a triangular Bezier patch in matlab

I need a program with a triangular Bezier patch in matlab

Answer 1

[Naga]

Hello Amina,

Creating a triangular Bézier patch involves defining a Bézier surface using a set of control points arranged in a triangular grid. A triangular Bézier patch is a type of Bézier surface that is defined over a triangular domain, typically parameterized by barycentric coordinates.

Here's a basic example of how you can create and visualize a triangular Bézier patch:

function triangularBezierPatch()
    % Define control points for a quadratic triangular Bézier patch
    controlPoints = [0, 0, 0; 1, 0, 0; 0, 1, 0; 0.5, 0.5, 1];
    degree = 2;

    % Generate barycentric coordinates
    [u, v] = meshgrid(linspace(0, 1, 20));
    w = 1 - u - v;
    valid = (w >= 0);
    u = u(valid); v = v(valid); w = w(valid);

    % Compute Bézier patch points
    points = computeBezierPatch(controlPoints, degree, u, v, w);

    % Plot Bézier patch
    trisurf(delaunay(u, v), points(:, 1), points(:, 2), points(:, 3), ...
            'FaceColor', 'cyan', 'EdgeColor', 'none');
    hold on;
    plot3(controlPoints(:, 1), controlPoints(:, 2), controlPoints(:, 3), ...
          'ro', 'MarkerSize', 8, 'LineWidth', 2);
    title('Triangular Bézier Patch');
    axis equal; grid on; view(3);xlabel('X');ylabel('Y');zlabel('Z');
end

function points = computeBezierPatch(controlPoints, degree, u, v, w)
    % Compute points on the Bézier patch given barycentric coordinates
    numPoints = length(u);
    numControlPoints = size(controlPoints, 1);
    points = zeros(numPoints, 3);

    % Compute Bernstein polynomials for the triangular Bézier patch
    B = zeros(numPoints, numControlPoints);
    index = 1;
    for i = 0:degree
        for j = 0:(degree - i)
            k = degree - i - j;
            B(:, index) = nchoosek(degree, i) * nchoosek(degree - i, j) .* ...
                          (u .^ i) .* (v .^ j) .* (w .^ k);
            index = index + 1;
        end
    end

    % Compute the Bézier surface points
    for i = 1:numControlPoints
        points = points + B(:, i) * controlPoints(i, :);
    end
end

1. Define a set of control points arranged in a triangular grid. Here a quadratic patch is used, which requires 6 control points.
2. Use barycentric coordinates (u, v, w) to parameterize the triangular domain.
3. Compute the Bernstein basis polynomials for the triangular Bézier patch.
4. Calculate the points on the Bézier patch using the Bernstein polynomials and control points.
5. Use 'trisurf' function to visualize the Bézier patch and plot the control points.

This code provides a simple framework for generating and visualizing a triangular Bézier patch. You can modify the control points and degree to create different patches.