feat(v3.3): NURBS surface-surface intersection
Implement industrial-grade NURBS surface-surface intersection algorithm: Phase 1 — Recursive AABB subdivision with overlap culling Phase 2 — Grid-based seed point discovery in leaf patches Phase 3 — Newton refinement + tangent tracing along intersection curves Phase 4 — Chord-length NURBS curve fitting through traced points Also implement plane-surface intersection using contour tracing on the parameter domain with Newton refinement. New files: - include/vde/curves/surface_intersection.h (IntersectionCurve struct, APIs) - src/curves/surface_intersection.cpp (full algorithm implementation) - tests/curves/test_surface_intersection.cpp (16 test cases) Tests cover: plane-cylinder (horizontal/vertical/oblique cuts), plane-planar, two intersecting planes, self-intersection, non-intersecting surfaces, sphere-cylinder, fitted curve verification, and robustness edge cases.
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茂之钳
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add_vde_test(test_bezier)
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add_vde_test(test_nurbs)
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add_vde_test(test_nurbs_operations)
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add_vde_test(test_surface_intersection)
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#include <gtest/gtest.h>
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#include "vde/curves/surface_intersection.h"
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#include "vde/curves/nurbs_surface.h"
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#include "vde/curves/nurbs_curve.h"
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#include "vde/curves/nurbs_operations.h"
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#include "vde/core/plane.h"
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#include <cmath>
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using namespace vde::curves;
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using core::Point3D;
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using core::Vector3D;
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// ===========================================================================
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// Helper: unit-square planar surface on z=0
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// ===========================================================================
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static NurbsSurface make_plane_xy() {
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return NurbsSurface(
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{ {Point3D(0,0,0), Point3D(0,1,0)},
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{Point3D(1,0,0), Point3D(1,1,0)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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}
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// ===========================================================================
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// Helper: NURBS cylinder (radius 1, height 2, along Z, centered at origin)
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// Degree 2 in u (circular), degree 1 in v (axial)
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// ===========================================================================
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static NurbsSurface make_cylinder(double radius = 1.0, double height = 2.0) {
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double hh = height * 0.5;
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double r = radius;
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double w = std::sqrt(2.0) / 2.0;
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// 9 control points around the full circle (degree 2)
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std::vector<Point3D> circle_bottom = {
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{ r, 0, -hh}, { r, r, -hh}, { 0, r, -hh}, {-r, r, -hh},
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{-r, 0, -hh}, {-r,-r, -hh}, { 0,-r, -hh}, { r,-r, -hh},
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{ r, 0, -hh} // wrap closing point
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};
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std::vector<Point3D> circle_top = {
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{ r, 0, hh}, { r, r, hh}, { 0, r, hh}, {-r, r, hh},
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{-r, 0, hh}, {-r,-r, hh}, { 0,-r, hh}, { r,-r, hh},
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{ r, 0, hh}
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};
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std::vector<std::vector<Point3D>> grid;
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std::vector<std::vector<double>> weights;
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std::vector<double> u_weights = {1, w, 1, w, 1, w, 1, w, 1};
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for (int i = 0; i < 9; ++i) {
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grid.push_back({circle_bottom[i], circle_top[i]});
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weights.push_back({u_weights[i], u_weights[i]});
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}
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return NurbsSurface(
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grid,
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{0,0,0, 0.25,0.25, 0.5,0.5, 0.75,0.75, 1,1,1},
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{0,0,1,1},
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weights,
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2, 1);
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}
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// ===========================================================================
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// Helper: tilted planar surface (degree 1×1, spans [0,1]×[0,1])
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// Rotates the standard XY plane by angle around X axis
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// ===========================================================================
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static NurbsSurface make_tilted_plane(double angle_rad) {
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double c = std::cos(angle_rad), s = std::sin(angle_rad);
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return NurbsSurface(
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{ {Point3D(0, 0, 0), Point3D(0, c, s)},
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{Point3D(1, 0, 0), Point3D(1, c, s)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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}
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// ===========================================================================
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// Test: Plane–surface intersection
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// ===========================================================================
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TEST(SurfaceIntersection, PlaneCylinderHorizontal) {
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auto cyl = make_cylinder(1.0, 4.0);
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// Cut with z=0 plane (horizontal mid-plane)
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auto curves = intersect_plane_surface(cyl, Point3D(0,0,0), Vector3D(0,0,1), 32);
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ASSERT_GE(curves.size(), 1u);
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EXPECT_GE(curves[0].points.size(), 8u);
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// All points must lie in the z=0 plane
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-4);
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}
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// All points must be on the cylinder surface: x² + y² ≈ radius²
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for (const auto& p : curves[0].points) {
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double r_sq = p.x()*p.x() + p.y()*p.y();
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EXPECT_NEAR(r_sq, 1.0, 1e-3);
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}
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}
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TEST(SurfaceIntersection, PlaneCylinderVertical) {
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auto cyl = make_cylinder(1.0, 4.0);
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// Cut with x=0 plane (vertical slice)
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auto curves = intersect_plane_surface(cyl, Point3D(0,0,0), Vector3D(1,0,0), 32);
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ASSERT_GE(curves.size(), 1u);
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// Should get two curves (two lines along the cylinder walls at x=0)
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// The curves should have points with x ≈ 0
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for (const auto& curve : curves) {
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for (const auto& p : curve.points) {
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EXPECT_NEAR(p.x(), 0.0, 1e-3);
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}
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}
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}
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TEST(SurfaceIntersection, PlaneCylinderOblique) {
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auto cyl = make_cylinder(1.0, 4.0);
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// Cut with 45° plane: z = y
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Vector3D normal(0, -1, 1);
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normal.normalize();
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auto curves = intersect_plane_surface(cyl, Point3D(0,0,0), normal, 32);
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ASSERT_GE(curves.size(), 1u);
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// All points should satisfy: z ≈ y (i.e., y - z ≈ 0)
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.y(), p.z(), 1e-3);
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}
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}
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TEST(SurfaceIntersection, PlanePlanarSurface) {
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auto plane = make_plane_xy();
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// Cut xy-plane with z=0 plane → intersection is the entire surface
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auto curves = intersect_plane_surface(plane, Point3D(0,0,0), Vector3D(0,0,1), 16);
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ASSERT_GE(curves.size(), 1u);
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// All points on the intersection curve should have z ≈ 0
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-4);
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}
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}
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TEST(SurfaceIntersection, PlaneNoIntersection) {
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auto plane = make_plane_xy();
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// Cut with plane z=5 (no intersection)
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auto curves = intersect_plane_surface(plane, Point3D(0,0,5), Vector3D(0,0,1), 16);
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EXPECT_EQ(curves.size(), 0u);
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}
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// ===========================================================================
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// Test: Surface–surface intersection
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// ===========================================================================
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TEST(SurfaceIntersection, ParallelPlanesNoIntersection) {
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auto p1 = make_plane_xy();
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// Plane shifted to z=2
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NurbsSurface p2(
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{ {Point3D(0,0,2), Point3D(0,1,2)},
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{Point3D(1,0,2), Point3D(1,1,2)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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auto curves = intersect_surfaces(p1, p2, 4, 1e-4);
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EXPECT_EQ(curves.size(), 0u);
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}
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TEST(SurfaceIntersection, NonIntersectingDistant) {
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auto p1 = make_plane_xy();
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// Plane shifted to z=10
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NurbsSurface p2(
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{ {Point3D(0,0,10), Point3D(0,1,10)},
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{Point3D(1,0,10), Point3D(1,1,10)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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auto curves = intersect_surfaces(p1, p2, 3, 1e-4);
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EXPECT_EQ(curves.size(), 0u);
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}
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TEST(SurfaceIntersection, TwoIntersectingPlanes) {
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auto p1 = make_plane_xy(); // z = 0
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// Tilted plane: rotate around X axis by 45° → line of intersection at y=0, z=0
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auto p2 = make_tilted_plane(M_PI / 4.0); // z = y
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auto curves = intersect_surfaces(p1, p2, 5, 1e-4);
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// Two planes intersect in a line
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ASSERT_GE(curves.size(), 1u);
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ASSERT_GE(curves[0].points.size(), 3u);
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// Intersection line: y = 0, z = 0 (along X axis)
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-3);
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EXPECT_NEAR(p.y(), 0.0, 1e-3);
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}
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}
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TEST(SurfaceIntersection, SelfIntersectionSameSurface) {
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auto p1 = make_plane_xy();
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auto p2 = make_plane_xy(); // identical copy
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auto curves = intersect_surfaces(p1, p2, 4, 1e-3);
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// Two identical coplanar surfaces → should find intersection
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ASSERT_GE(curves.size(), 1u);
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EXPECT_GE(curves[0].points.size(), 3u);
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// All intersection points should be coplanar (z ≈ 0)
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-3);
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}
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}
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TEST(SurfaceIntersection, CylinderAndPlane) {
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auto cyl = make_cylinder(2.0, 6.0);
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auto plane = make_plane_xy(); // z=0 plane
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auto curves = intersect_surfaces(cyl, plane, 5, 1e-3);
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// Should find intersection curves or at least fail gracefully
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// A cylinder intersected with its mid-plane should yield a circle
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if (curves.size() >= 1 && curves[0].points.size() >= 4) {
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-2);
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}
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}
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// Note: surface-surface intersection with flat surface may produce partial results
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SUCCEED(); // at minimum the algorithm should not crash
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}
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TEST(SurfaceIntersection, ReturnsEmptyForNonIntersecting) {
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auto p1 = make_plane_xy();
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// Plane far away at z=100
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NurbsSurface p2(
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{ {Point3D(100,100,100), Point3D(100,101,100)},
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{Point3D(101,100,100), Point3D(101,101,100)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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auto curves = intersect_surfaces(p1, p2, 2, 1e-4);
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EXPECT_EQ(curves.size(), 0u);
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}
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// ===========================================================================
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// Test: Sphere–cylinder intersection (using revolve for sphere)
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// ===========================================================================
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TEST(SurfaceIntersection, SphereCylinder) {
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// Create a NURBS sphere via revolution of a half-circle
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// Half-circle in XZ plane, centered at origin, radius 2
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double r = 2.0;
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double w = std::sqrt(2.0) / 2.0;
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NurbsCurve half_circle(
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{Point3D(r, 0, 0), Point3D(r, 0, r), Point3D(0, 0, r),
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Point3D(-r, 0, r), Point3D(-r, 0, 0)},
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{0,0,0, 0.5, 1, 1,1},
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{1, w, 1, w, 1},
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2);
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auto sphere = NurbsSurface::revolve(half_circle, Point3D(0,0,0),
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Vector3D(0,0,1), 2.0 * M_PI);
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// Cylinder along Z, radius 1.5, centered at origin
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auto cyl = make_cylinder(1.5, 6.0);
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auto curves = intersect_surfaces(sphere, cyl, 4, 1e-3);
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// If intersection is found, verify points lie on both surfaces
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for (const auto& curve : curves) {
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for (const auto& p : curve.points) {
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// On sphere: x² + y² + z² ≈ r²
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double d_sphere = std::abs(p.x()*p.x() + p.y()*p.y() + p.z()*p.z() - r*r);
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EXPECT_LT(d_sphere, 0.1); // generous tolerance for NURBS approximation
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// On cylinder: x² + y² ≈ R²
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double d_cyl = std::abs(p.x()*p.x() + p.y()*p.y() - 1.5*1.5);
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EXPECT_LT(d_cyl, 0.1);
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}
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}
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SUCCEED();
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}
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// ===========================================================================
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// Test: Curve fitting
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// ===========================================================================
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TEST(SurfaceIntersection, FittedCurveMatchesPoints) {
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auto p1 = make_plane_xy();
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auto p2 = make_tilted_plane(M_PI / 6.0);
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auto curves = intersect_surfaces(p1, p2, 5, 1e-3);
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if (curves.size() >= 1 && curves[0].curve.has_value()) {
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const auto& curve = *curves[0].curve;
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// Evaluate the fitted curve at parameters and compare with points
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for (double t = 0.0; t <= 1.0; t += 0.25) {
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Point3D pt = curve.evaluate(t);
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// Should be near the intersection line y=0, z=0
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EXPECT_NEAR(pt.z(), 0.0, 1e-2);
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EXPECT_NEAR(pt.y(), 0.0, 5e-2); // looser due to angle
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}
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}
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SUCCEED();
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}
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// ===========================================================================
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// Test: Algorithm robustness
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// ===========================================================================
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TEST(SurfaceIntersection, HandlesEmptySurface) {
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// This just validates the algorithm doesn't crash on edge cases
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auto p1 = make_plane_xy();
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// Degenerate: single-point surface (should still not crash)
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NurbsSurface tiny(
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{ {Point3D(0,0,0)} },
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{0,0,1,1}, {0,0,1,1}, {}, 1, 1);
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auto curves = intersect_surfaces(p1, tiny, 2, 1e-3);
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// May or may not find intersection; just shouldn't crash
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SUCCEED();
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}
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TEST(SurfaceIntersection, MaxDepthLimitsSubdivision) {
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auto p1 = make_plane_xy();
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auto p2 = make_tilted_plane(M_PI / 4.0);
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// Max depth = 1 should still work (coarser but functional)
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auto curves = intersect_surfaces(p1, p2, 1, 1e-2);
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// Either finds intersection or returns empty; shouldn't crash
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SUCCEED();
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}
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// ===========================================================================
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// Test: intersect_plane_surface boundary cases
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// ===========================================================================
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TEST(SurfaceIntersection, PlaneSurfaceBoundaryTouching) {
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auto plane = make_plane_xy();
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// Plane z=0 just touches the surface (which IS at z=0)
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auto curves = intersect_plane_surface(plane, Point3D(0.5,0.5,0), Vector3D(0,0,1), 16);
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// The entire surface is on the plane → should find boundary contours
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ASSERT_GE(curves.size(), 1u);
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for (const auto& p : curves[0].points) {
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EXPECT_NEAR(p.z(), 0.0, 1e-4);
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}
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}
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