1、示例一：计算多边形域的近似中间。本示例说明了如何使用约众龊受礻束的Delaunay三角剖分来创建多边形域的近似中间轴。多边形的中间轴由多舍膺雕沆边形内部最大磁盘中心的轨迹定义。程序如下：% Construct a constrained Delaunay triangulation of a sample of points% on the domain boundary.load trimesh2ddt = delaunayTriangulation(x,y,Constraints);inside = dt.isInterior();% Construct a triangulation to represent the domain triangles.tr = triangulation(dt(inside, :), dt.Points);% Construct a set of edges that join the circumcenters of neighboring% triangles; the additional logic constructs a unique set of such edges.numt = size(tr,1);T = (1:numt)';neigh = tr.neighbors();cc = tr.circumcenter();xcc = cc(:,1);ycc = cc(:,2);idx1 = T < neigh(:,1);idx2 = T < neigh(:,2);idx3 = T < neigh(:,3);neigh = [T(idx1) neigh(idx1,1); T(idx2) neigh(idx2,2); T(idx3) neigh(idx3,3)]';% Plot the domain triangles in green, the domain boundary in blue and the% medial axis in red.clf;triplot(tr, 'g');hold on;plot(xcc(neigh), ycc(neigh), '-r', 'LineWidth', 1.5);axis([-10 310 -10 310]);axis equal;plot(x(Constraints'),y(Constraints'), '-b', 'LineWidth', 1.5);xlabel('Medial Axis of a Polygonal Domain', 'fontweight','b');hold off;按“Enter”键。如图1所示。
2、示例二：将2D网格变形为修改后的边界此示例显示如何变形2D域的网格以适应对域边界的修改。步骤1：加载数据。 要变形的网格由trife，xfe，yfe定义，它是面顶点格式的三角剖分。程序如下：load trimesh2dclf;triplot(trife,xfe,yfe);axis equal;axis([-10 310 -10 310]);axis equal;xlabel('Initial Mesh', 'fontweight','b');按“Enter”键。如图2所示。
3、步骤2：构造背景三角剖分-代表网格边界的点集的约束Delaunay三角剖分。 对于网格的每个顶点，计算一个描述符，以定义其相对于背景三角剖分的位置。 描述子是包围的三角形以及相对于该三角形的重心坐标。程序入下：dt = delaunayTriangulation(x,y,Constraints);clf;triplot(dt);axis equal;axis([-10 310 -10 310]);axis equal;xlabel('Background Triangulation', 'fontweight','b');descriptors.tri = pointLocation(dt,xfe, yfe);descriptors.baryCoords = cartesianToBarycentric(dt,descriptors.tri, [xfe yfe]);按“Enter”键。如图3所示。
4、步骤3：编辑背景三角剖分，以将所需的修改合并到域边界。程序如下：cc1 = [210 90];circ1 = (143:180)';x(circ1) = (x(circ1)-cc1(1))*0.6 + cc1(1);y(circ1) = (y(circ1)-cc1(2))*0.6 + cc1(2);tr = triangulation(dt(:,:),x,y);clf;triplot(tr);axis([-10 310 -10 310]);axis equal;xlabel('Edited Background Triangulation - Hole Size Reduced', 'fontweight','b');按“Enter”键。如图4所示。
5、步骤4：使用变形的背景三角剖分作为评估的基础，将描述符转换回笛卡尔坐标。程序入下：Xnew = barycentricToCartesian(tr,descriptors.tri, descriptors.baryCoords);tr = triangulation(trife, Xnew);clf;triplot(tr);axis([-10 310 -10 310]);axis equal;xlabel('Morphed Mesh', 'fontweight','b');按“Enter”键。如图5所示。
