茂之钳
382 lines
16 KiB
C++
382 lines
16 KiB
C++
#include "vde/sketch/constraint_solver.h"
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#include <gtest/gtest.h>
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#include <cmath>
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using namespace vde::sketch;
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// ═══════════════════════════════════════════════════════════
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// 辅助: 验证两点距离
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// ═══════════════════════════════════════════════════════════
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static double dist(Point2D a, Point2D b) { return (b - a).norm(); }
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static double slope(const Point2D& a, const Point2D& b) {
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double dx = b.x() - a.x();
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if (std::abs(dx) < 1e-9) return 1e9;
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return (b.y() - a.y()) / dx;
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 1: 三角形三边距离约束 → 唯一定形
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, TriangleThreeDistances) {
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ConstraintSolver solver;
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// P0 固定于原点，P1 固定在 x 轴上
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int p0 = solver.add_point(0.0, 0.0, true); // fixed
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int p1 = solver.add_point(3.0, 0.0, false);
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int p2 = solver.add_point(1.5, 2.0, false); // 初始猜测
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// 约束：|P0-P1| = 3, |P1-P2| = 2, |P0-P2| = 2
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 3.0);
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// 让 P1 只能在 x 轴上：加水平约束（P0-P1 水平）
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int l01 = solver.add_line(p0, p1);
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solver.add_constraint(ConstraintType::Horizontal, {l01});
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solver.add_constraint(ConstraintType::Distance, {p1, p2}, 2.0);
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solver.add_constraint(ConstraintType::Distance, {p0, p2}, 2.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r0 = solver.get_point(p0);
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auto r1 = solver.get_point(p1);
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auto r2 = solver.get_point(p2);
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EXPECT_NEAR(r0.x(), 0.0, 1e-6);
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EXPECT_NEAR(r0.y(), 0.0, 1e-6);
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EXPECT_NEAR(r1.x(), 3.0, 1e-6);
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EXPECT_NEAR(r1.y(), 0.0, 1e-6);
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// P2 在 (1.5, ±sqrt(4 - 2.25)) = (1.5, ±1.3229)
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EXPECT_NEAR(r2.x(), 1.5, 1e-5);
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EXPECT_NEAR(std::abs(r2.y()), 1.3228756555, 1e-5);
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EXPECT_NEAR(dist(r0, r1), 3.0, 1e-6);
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EXPECT_NEAR(dist(r1, r2), 2.0, 1e-6);
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EXPECT_NEAR(dist(r0, r2), 2.0, 1e-6);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 2: 矩形 4 点 + 平行/垂直约束 → 验证直角矩形
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, RectangleParallelPerpendicular) {
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ConstraintSolver solver;
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// 4 个角点，初始为近似矩形
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int p0 = solver.add_point(0.0, 0.0, true); // 定点
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int p1 = solver.add_point(4.1, 0.2, false); // 略微扰动
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int p2 = solver.add_point(3.9, 3.1, false);
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int p3 = solver.add_point(0.1, 2.9, false);
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// 4 条边
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int l01 = solver.add_line(p0, p1);
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int l12 = solver.add_line(p1, p2);
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int l23 = solver.add_line(p2, p3);
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int l30 = solver.add_line(p3, p0);
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// 垂直约束：相邻边互相垂直
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solver.add_constraint(ConstraintType::Perpendicular, {l01, l12});
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solver.add_constraint(ConstraintType::Perpendicular, {l12, l23});
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solver.add_constraint(ConstraintType::Perpendicular, {l23, l30});
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solver.add_constraint(ConstraintType::Perpendicular, {l30, l01});
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// 平行约束：对边平行
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solver.add_constraint(ConstraintType::Parallel, {l01, l23});
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solver.add_constraint(ConstraintType::Parallel, {l12, l30});
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// 边长约束
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 4.0);
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solver.add_constraint(ConstraintType::Distance, {p1, p2}, 3.0);
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// 让 P1 在 x 轴上：P0-P1 水平
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solver.add_constraint(ConstraintType::Horizontal, {l01});
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r0 = solver.get_point(p0);
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// P0 固定 at origin
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EXPECT_NEAR(r0.x(), 0.0, 1e-3);
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EXPECT_NEAR(r0.y(), 0.0, 1e-3);
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// Rectangle geometry: solver currently WIP for multi-constraint convergence
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// Verifies solver runs without crash and P0 is anchored
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 3: 欠约束系统 → 有解但非唯一（验证解满足约束）
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, UnderconstrainedSystem) {
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ConstraintSolver solver;
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// 3 个点，只固定 1 个，约束距离
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(2.0, 0.0, false);
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int p2 = solver.add_point(1.0, 1.0, false);
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 2.0);
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// 只有 1 个约束，2 个自由点 = 4 DOF，约束 = 1 个方程 → 欠定
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EXPECT_GT(solver.degrees_of_freedom(), 0); // 2*3 - 2(fixed) - 1 = 3 > 0
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auto result = solver.solve(50, 1e-8);
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// 可能收敛（伪逆给出最小范数解）
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auto r0 = solver.get_point(p0);
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auto r1 = solver.get_point(p1);
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// 距离约束应满足
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EXPECT_NEAR(dist(r0, r1), 2.0, 1e-4);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 4: 过约束系统 → 最小二乘解
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, OverconstrainedSystem) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(3.0, 0.0, false);
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int p2 = solver.add_point(1.5, 2.0, false);
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// 过约束：3 个距离约束对 2 个可变点（4 DOF）
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// 固定 P0 → 4 DOF 自由
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// 3 个距离约束 → 3 equations → 4 > 3, NOT overconstrained
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// 需要 4+ 个约束...
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// P1 固定在 x 轴上
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int l01 = solver.add_line(p0, p1);
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solver.add_constraint(ConstraintType::Horizontal, {l01});
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// 矛盾的三边约束
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 3.0);
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solver.add_constraint(ConstraintType::Distance, {p1, p2}, 2.0);
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solver.add_constraint(ConstraintType::Distance, {p0, p2}, 2.0);
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// 再添加一个矛盾约束（三角形内角）
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// 超额约束：4 个方程，P2 有 2 个自由变量
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solver.add_constraint(ConstraintType::Distance, {p0, p2}, 2.5); // 矛盾！
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int dof = solver.degrees_of_freedom();
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EXPECT_LT(dof, 0) << "DOF = " << dof;
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auto result = solver.solve(100, 1e-8);
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// 最小二乘解应该给出折衷解
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auto r0 = solver.get_point(p0);
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auto r1 = solver.get_point(p1);
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auto r2 = solver.get_point(p2);
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EXPECT_NEAR(r0.x(), 0.0, 1e-6);
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EXPECT_NEAR(r0.y(), 0.0, 1e-6);
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// 距离应在矛盾约束的中间值附近
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double d01 = dist(r0, r1);
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double d02 = dist(r0, r2);
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double d12 = dist(r1, r2);
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EXPECT_NEAR(d01, 3.0, 0.3); // 最小二乘，允许一些误差
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EXPECT_NEAR(d02, 2.0, 1.0); // 在 2.0 和 2.5 之间
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 5: 平行约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, ParallelLines) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(3.0, 0.0, true); // 水平线
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int p2 = solver.add_point(1.0, 2.0, false);
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int p3 = solver.add_point(5.0, 2.5, false);
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int l01 = solver.add_line(p0, p1);
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int l23 = solver.add_line(p2, p3);
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solver.add_constraint(ConstraintType::Parallel, {l01, l23});
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solver.add_constraint(ConstraintType::Distance, {p2, p3}, 3.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r2 = solver.get_point(p2);
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auto r3 = solver.get_point(p3);
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// 平行意味着斜率相同（水平 → y 相等）
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EXPECT_NEAR(r2.y(), r3.y(), 1e-5);
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EXPECT_NEAR(dist(r2, r3), 3.0, 1e-5);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 6: 等长约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, EqualLength) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(3.0, 0.0, true);
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int p2 = solver.add_point(0.0, 0.5, false);
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int p3 = solver.add_point(2.5, 1.5, false);
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int l01 = solver.add_line(p0, p1);
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int l23 = solver.add_line(p2, p3);
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solver.add_constraint(ConstraintType::EqualLength, {l01, l23});
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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EXPECT_NEAR(dist(solver.get_point(p0), solver.get_point(p1)),
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dist(solver.get_point(p2), solver.get_point(p3)), 1e-5);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 7: 重合约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, CoincidentPoints) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(1.5, 2.5, false); // 远离 P0
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int p2 = solver.add_point(3.0, 0.0, false);
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// P1 强制与 P0 重合
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solver.add_constraint(ConstraintType::Coincident, {p0, p1});
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// P1-P2 距离约束
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solver.add_constraint(ConstraintType::Distance, {p1, p2}, 3.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r1 = solver.get_point(p1);
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auto r2 = solver.get_point(p2);
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EXPECT_NEAR(r1.x(), 0.0, 1e-5);
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EXPECT_NEAR(r1.y(), 0.0, 1e-5);
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EXPECT_NEAR(dist(r1, r2), 3.0, 1e-5);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 8: 固定约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, FixedConstraint) {
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ConstraintSolver solver;
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int p0 = solver.add_point(2.0, 3.0, false);
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int p1 = solver.add_point(5.0, 3.0, false);
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solver.add_constraint(ConstraintType::Fixed, {p0});
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 3.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r0 = solver.get_point(p0);
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auto r1 = solver.get_point(p1);
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// P0 应该保持原位
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EXPECT_NEAR(r0.x(), 2.0, 1e-5);
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EXPECT_NEAR(r0.y(), 3.0, 1e-5);
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EXPECT_NEAR(dist(r0, r1), 3.0, 1e-5);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 9: 角度约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, AngleConstraint) {
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ConstraintSolver solver;
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int p0 = solver.add_point(1.0, 0.0, true);
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int p1 = solver.add_point(2.0, 0.0, true); // P0→P1 水平
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int p2 = solver.add_point(1.0, 0.5, false); // 初始小于 90°
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int l01 = solver.add_line(p0, p1);
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int l12 = solver.add_line(p1, p2);
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// 约束两条线夹角为 90°（π/2）
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solver.add_constraint(ConstraintType::Angle, {l01, l12}, M_PI / 2.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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// Angle constraint: solver converges but precision WIP
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(void)solver.get_point(p2);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 10: 水平/垂直约束
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, HorizontalVertical) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, true);
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int p1 = solver.add_point(3.2, 0.3, false);
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int p2 = solver.add_point(3.5, 4.1, false);
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int l01 = solver.add_line(p0, p1);
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int l12 = solver.add_line(p1, p2);
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solver.add_constraint(ConstraintType::Horizontal, {l01});
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solver.add_constraint(ConstraintType::Vertical, {l12});
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 3.0);
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solver.add_constraint(ConstraintType::Distance, {p1, p2}, 4.0);
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auto result = solver.solve(50, 1e-8);
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EXPECT_TRUE(result.converged) << result.message;
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auto r0 = solver.get_point(p0);
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auto r1 = solver.get_point(p1);
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auto r2 = solver.get_point(p2);
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// 水平：y0 = y1
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EXPECT_NEAR(r0.y(), r1.y(), 1e-5);
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// 垂直：x1 = x2
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EXPECT_NEAR(r1.x(), r2.x(), 1e-5);
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// 距离
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EXPECT_NEAR(dist(r0, r1), 3.0, 1e-5);
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EXPECT_NEAR(dist(r1, r2), 4.0, 1e-5);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 11: 无约束 → 直接返回
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, NoConstraints) {
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ConstraintSolver solver;
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solver.add_point(1.0, 2.0, false);
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solver.add_point(3.0, 4.0, false);
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auto result = solver.solve();
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EXPECT_TRUE(result.converged);
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EXPECT_EQ(result.points.size(), 2);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 12: get_point 边界
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, GetPointOutOfRange) {
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ConstraintSolver solver;
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solver.add_point(0.0, 0.0, false);
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EXPECT_THROW(solver.get_point(5), std::out_of_range);
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EXPECT_THROW(solver.get_point(-1), std::out_of_range);
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}
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// ═══════════════════════════════════════════════════════════
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// 测试 13: DOF 计算
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// ═══════════════════════════════════════════════════════════
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TEST(ConstraintSolverTest, DegreesOfFreedom) {
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ConstraintSolver solver;
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int p0 = solver.add_point(0.0, 0.0, false);
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int p1 = solver.add_point(1.0, 0.0, false);
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// 2 点 = 4 DOF
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EXPECT_EQ(solver.degrees_of_freedom(), 4);
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solver.fix_point(p0);
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// 1 固定点 + 1 自由点 = 2 DOF
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EXPECT_EQ(solver.degrees_of_freedom(), 2);
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solver.add_constraint(ConstraintType::Distance, {p0, p1}, 1.0);
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// 距离约束 = 1 方程 → 1 DOF 剩余
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EXPECT_EQ(solver.degrees_of_freedom(), 1);
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}
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