StuCanvas

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三维物体 ​

自由点 ​

cpp
import stucanvas;

using namespace StuCanvas;

STUCANVAS_MAIN(Canvas& canvas) {
    auto& graph = canvas.createSObjectGraph<double>();
    auto& p1 = graph.createFreePoint3D(1.0, 2.0, 3.0);
    auto& p2 = graph.createFreePoint3D(4.0, 5.0, 6.0);
    auto& p3 = graph.createFreePoint3D(7.0, 3.0, 2.0);
};

createFreePoint3D 创建三维自由点，参数为 (x, y, z)。与二维自由点相同，位于 DAG 叶子层，无几何约束。

平面 ​

平面对象由两个向量张成：第一个参数为起点，后两个参数为终点，三点构成空间中的平面区域。

cpp
import stucanvas;

using namespace StuCanvas;

STUCANVAS_MAIN(Canvas& canvas) {
    auto& graph = canvas.createSObjectGraph<double>();
    auto& a = graph.createFreePoint3D(0.0, 0.0, 0.0);
    auto& b = graph.createFreePoint3D(3.0, 0.0, 0.0);
    auto& c = graph.createFreePoint3D(0.0, 4.0, 0.0);
    auto& inf_plane = graph.createInfinitePlane_3D(a, b, c);
    auto& tri_plane = graph.createTrianglePlane_3D(a, b, c);
    auto& para_plane = graph.createParallelogramPlane_3D(a, b, c);
};
方法参数含义
createInfinitePlane_3D起点 + 两终点由两个向量张成的无限平面
createTrianglePlane_3D起点 + 两终点三点围成的三角形区域
createParallelogramPlane_3D起点 + 两终点起点与两向量张成的平行四边形区域

三个点均为 FreePoint3D 引用。点坐标变更时平面自动更新。

三维求解器 ​

三维空间中的直线创建方式与二维一致（createSegment2D → createSegment3D，createLine2D → createLine3D，createRay2D → createRay3D）。求解器对象的变化如下：

二维三维
createPerpendicularLine2DcreatePerpendicularPlane_3D（垂面）
createParallelLine2DcreateParallelPlane_3D（平行面）
—createNormalLine_3D（法线）
createTangentLine_2DcreateTangentLine_3D（切线）、createTangentPlane_3D（切平面）
createIntersectionPoint_2DcreateIntersectionPoint_3D（交点）
—createIntersectionCurve_3D（交线）

三维不再提供垂线和平行线，改为垂面和平行面（依赖面对象和点对象）。法线依赖面对象和点对象，过点垂直于面。三维切线作用于拓扑维度为 1 的曲线，切平面作用于拓扑维度为 2 的曲面（如球体）。交点仍可用，新增交线用于求解两个三维物体之间的相交曲线。

圆柱与圆锥 ​

cpp
import stucanvas;

using namespace StuCanvas;

STUCANVAS_MAIN(Canvas& canvas) {
    auto& graph = canvas.createSObjectGraph<double>();
    auto& a = graph.createFreePoint3D(0.0, 0.0, 0.0);
    auto& b = graph.createFreePoint3D(0.0, 0.0, 5.0);
    auto& c = graph.createFreePoint3D(0.0, 0.0, 3.0);
    auto& cylinder = graph.createCylinder_3D(a, b, 2.0);
    auto& cone = graph.createCone_3D(c, b, 30.0, 3.0);
};
方法参数含义
createCylinder_3D两中心点 + 半径两点定义中心轴方向，半径定义柱体粗细
createCone_3D两中心点 + 张角 + 高度两点定义中心轴方向，张角（度）和高度定义锥体形状

球体 ​

cpp
import stucanvas;

using namespace StuCanvas;

STUCANVAS_MAIN(Canvas& canvas) {
    auto& graph = canvas.createSObjectGraph<double>();
    auto& a = graph.createFreePoint3D(1.0, 0.0, 0.0);
    auto& b = graph.createFreePoint3D(0.0, 1.0, 0.0);
    auto& c = graph.createFreePoint3D(0.0, 0.0, 1.0);
    auto& center = graph.createFreePoint3D(0.0, 0.0, 0.0);
    auto& s1 = graph.createSphere_3D_Radius(center, 4.0);
    auto& s2 = graph.createSphere_3D_4Points(a, b, c, center);
};
方法参数含义
createSphere_3D_Radius球心 + 半径球心点与半径值
createSphere_3D_4Points四个点四点确定一个球体

柏拉图多面体 ​

cpp
import stucanvas;

using namespace StuCanvas;

STUCANVAS_MAIN(Canvas& canvas) {
    auto& graph = canvas.createSObjectGraph<double>();
    auto& center = graph.createFreePoint3D(0.0, 0.0, 0.0);
    auto& tetra = graph.createTetrahedron_3D(center, 2.0);
    auto& cube = graph.createCube_3D(center, 2.0);
    auto& octa = graph.createOctahedron_3D(center, 2.0);
    auto& dodeca = graph.createDodecahedron_3D(center, 2.0);
    auto& icosa = graph.createIcosahedron_3D(center, 2.0);
};

面数内置于函数名，参数为中心点和边长：

方法面数
createTetrahedron_3D4（正四面体）
createCube_3D6（正六面体）
createOctahedron_3D8（正八面体）
createDodecahedron_3D12（正十二面体）
createIcosahedron_3D20（正二十面体）