| // Copyright 2018 The Fuchsia Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| // TODO(ES-139): make GLM_FORCE_RADIANS the default. We rely on this below for |
| // creating quaternions. |
| #define GLM_FORCE_RADIANS |
| #include <glm/gtc/quaternion.hpp> |
| |
| #include "lib/escher/geometry/plane_ops.h" |
| |
| #include "lib/escher/geometry/intersection.h" |
| #include "lib/escher/geometry/transform.h" |
| #include "lib/escher/geometry/type_utils.h" |
| |
| #include "gtest/gtest.h" |
| |
| namespace { |
| |
| using namespace escher; |
| |
| TEST(plane3, PointOnPlaneConstructor) { |
| std::vector<float> vals{0, 1, -1, 2, -2, 3, -3, 4, -4}; |
| size_t vals_size = vals.size(); |
| for (size_t i = 0; i < vals_size; ++i) { |
| for (size_t j = 0; j < vals_size; ++j) { |
| for (size_t k = 1; k < vals_size; ++k) { |
| vec3 pt(vals[i], vals[j], vals[k]); |
| vec3 dir = glm::normalize(pt); |
| |
| // Verify that both constructors yield the same result for planes |
| // through the origin. |
| EXPECT_EQ(plane3(dir, 0), plane3(vec3(0, 0, 0), dir)); |
| |
| // Verify that both constructors yield the same result for planes |
| // passing through the chosen point |
| plane3 plane_through_point(dir, glm::length(pt)); |
| plane3 plane_through_point2(pt, dir); |
| EXPECT_EQ(plane_through_point.dir(), plane_through_point2.dir()); |
| EXPECT_NEAR(plane_through_point.dist(), plane_through_point2.dist(), |
| kEpsilon); |
| |
| // Pick 3 other points on the same plane, and verify that they result in |
| // the same plane through the point. |
| if (i != 0 && j != 0) { |
| vec3 ortho1 = glm::normalize(vec3(-vals[j], vals[i], 0)); |
| vec3 ortho2 = glm::cross(ortho1, dir); |
| plane3 p1(pt + ortho1, dir); |
| plane3 p2(pt + ortho2, dir); |
| plane3 p12(pt + ortho1 + ortho2, dir); |
| EXPECT_NEAR(plane_through_point.dist(), p1.dist(), kEpsilon); |
| EXPECT_NEAR(plane_through_point.dist(), p2.dist(), kEpsilon); |
| EXPECT_NEAR(plane_through_point.dist(), p12.dist(), kEpsilon); |
| } |
| } |
| } |
| } |
| } |
| |
| TEST(plane2, Clipping) { |
| vec2 pt1(0.4f, 100.f); |
| vec2 pt2(0.4f, -100.f); |
| vec2 pt3(0.6f, 100.f); |
| vec2 pt4(0.6f, -100.f); |
| |
| { |
| // 0.4 is to the left of the plane and 0.6 is to the right. |
| plane2 pl(vec2(1.f, 0.f), 0.5f); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt1)); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt2)); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt3)); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt4)); |
| } |
| |
| { |
| // Same plane, different orientation. |
| plane2 pl(vec2(-1.f, 0.f), -0.5f); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt1)); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt2)); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt3)); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt4)); |
| } |
| |
| { |
| // Non-axis-aligned plane through the origin. |
| plane2 pl(glm::normalize(vec2(1.f, -1.f)), 0); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt1)); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt2)); |
| EXPECT_TRUE(PlaneClipsPoint(pl, pt3)); |
| EXPECT_FALSE(PlaneClipsPoint(pl, pt4)); |
| } |
| |
| { |
| // Non-axis-aligned plane offset from the origin. |
| plane2 pl(glm::normalize(vec2(1.f, -1.f)), 100.f); |
| // Length of the projection of the plane vector on the coordinate axes (same |
| // for both because the slope is -1). |
| const float axis_project = sqrt(100.f * 100.f / 2); |
| // Double |axis_project| because the plane tangent is vec2(-1.f, 1.f). |
| const float axis_intersect = 2.f * axis_project; |
| |
| EXPECT_FALSE(PlaneClipsPoint(pl, vec2(axis_intersect * 1.01f, 0.f))); |
| EXPECT_FALSE(PlaneClipsPoint(pl, vec2(0.f, axis_intersect * -1.01f))); |
| EXPECT_FALSE( |
| PlaneClipsPoint(pl, vec2(axis_project, -axis_project) * 1.01f)); |
| EXPECT_TRUE(PlaneClipsPoint(pl, vec2(axis_intersect * 0.99f, 0.f))); |
| EXPECT_TRUE(PlaneClipsPoint(pl, vec2(0.f, axis_intersect * -0.99f))); |
| EXPECT_TRUE(PlaneClipsPoint(pl, vec2(axis_project, -axis_project) * 0.99f)); |
| } |
| } |
| |
| // Shorter version of 2D plane clipping. |
| TEST(plane3, Clipping) { |
| const vec3 plane_vec = glm::normalize(vec3(-1.f, -1.f, -1.f)); |
| const float plane_distance = -100.f; |
| const plane3 plane(plane_vec, plane_distance); |
| |
| const float axis_project = plane_vec.x * plane_distance; |
| EXPECT_EQ(axis_project, plane_vec.y * plane_distance); |
| EXPECT_EQ(axis_project, plane_vec.y * plane_distance); |
| |
| EXPECT_TRUE(PlaneClipsPoint( |
| plane, vec3(axis_project, axis_project, axis_project) * 1.01f)); |
| EXPECT_FALSE(PlaneClipsPoint( |
| plane, vec3(axis_project, axis_project, axis_project) * 0.99f)); |
| |
| // Let's say that (1,1,1) is a point on the plane parallel to our plane (i.e. |
| // same normal, but different distance to origin). What is the point (x,0,0) |
| // where the plane intersects the x-axis? The vector to this point is |
| // (x-1,-1,-1), and since this vector must be perpendicular to (1,1,1), their |
| // dot product must equal zero. Therefore x - 1 - 1 -1 == 0, so x == 3. |
| // Since (1,1,1) isn't a point on our plane, but axis_project * (1,1,1) is, we |
| // have the following: |
| const float axis_intersect = 3 * axis_project; |
| EXPECT_TRUE(PlaneClipsPoint(plane, vec3(axis_intersect, 0.f, 0.f) * 1.01f)); |
| EXPECT_TRUE(PlaneClipsPoint(plane, vec3(0.f, axis_intersect, 0.f) * 1.01f)); |
| EXPECT_TRUE(PlaneClipsPoint(plane, vec3(0.f, 0.f, axis_intersect) * 1.01f)); |
| EXPECT_FALSE(PlaneClipsPoint(plane, vec3(axis_intersect, 0.f, 0.f) * 0.99f)); |
| EXPECT_FALSE(PlaneClipsPoint(plane, vec3(0.f, axis_intersect, 0.f) * 0.99f)); |
| EXPECT_FALSE(PlaneClipsPoint(plane, vec3(0.f, 0.f, axis_intersect) * 0.99f)); |
| } |
| |
| // Helper function for Intersection tests. |
| template <typename PlaneT, typename VecT> |
| float TestPlaneIntersection(PlaneT plane, VecT pt1, VecT pt2) { |
| VecT seg_vec = pt2 - pt1; |
| const float t1 = IntersectLinePlane(pt1, seg_vec, plane); |
| const float t2 = IntersectLinePlane(pt2, -seg_vec, plane); |
| if (t1 == FLT_MAX || t2 == FLT_MAX) { |
| EXPECT_EQ(t1, t2); |
| return t1; |
| } |
| |
| float seg_vec_length_squared = glm::dot(seg_vec, seg_vec); |
| |
| // TODO(ES-137): revisit kEpsilon fudge-factor. |
| EXPECT_NEAR(1.f, t1 + t2, kEpsilon * seg_vec_length_squared); |
| |
| const VecT intersection = pt1 + t1 * (pt2 - pt1); |
| const VecT plane_def_vec = plane.dir() * plane.dist(); |
| const VecT vec_on_plane = intersection - plane_def_vec; |
| // TODO(ES-137): revisit kEpsilon fudge-factor. |
| if (glm::dot(vec_on_plane, vec_on_plane) > kEpsilon * 10) { |
| // If the distance is great enough, verify that the intersection really is |
| // on the plane. |
| // TODO(ES-137): revisit kEpsilon fudge-factor. |
| EXPECT_LT(glm::dot(vec_on_plane, plane.dir()), kEpsilon * 100); |
| } |
| |
| return t1; |
| } |
| |
| TEST(plane2, Intersection) { |
| // This is covered sufficiently by the 3D test, since IntersectLinePlane() is |
| // implemented generically: it does not depend on the dimensionality of the |
| // vector space. |
| } |
| |
| TEST(plane3, Intersection) { |
| // Generate a plethora of "should intersect" cases by geometric construction. |
| for (float origin_dist = -400.f; origin_dist <= 400.f; origin_dist += 100.f) { |
| for (float radians = 0.f; radians <= 2 * M_PI; radians += M_PI / 5.9) { |
| const vec3 plane_normal = |
| glm::normalize(vec3(cos(radians), sin(radians), 0.5f)); |
| const plane3 plane(plane_normal, origin_dist); |
| const vec3 plane_origin = plane.dir() * plane.dist(); |
| const vec3 tangent(-plane.dir().y, plane.dir().x, 0.f); |
| const vec3 bitangent_mix = |
| 0.5f * (tangent + glm::cross(plane.dir(), tangent)); |
| |
| // Compute some points on the plane, and then use the plane normal to |
| // generate some points off the plane. |
| for (float on_plane_dist = -50.f; on_plane_dist < 50.f; |
| on_plane_dist += 5.f) { |
| vec3 point_on_plane = plane_origin + bitangent_mix * on_plane_dist; |
| |
| for (float dist_between_off_plane_points = -55.f; |
| dist_between_off_plane_points <= 55.f; |
| dist_between_off_plane_points += 10.f) { |
| for (float straddle_factor = 0.1f; straddle_factor <= 0.9f; |
| straddle_factor += 0.2f) { |
| vec3 pt1 = point_on_plane + straddle_factor * |
| dist_between_off_plane_points * |
| plane.dir(); |
| vec3 pt2 = point_on_plane + (straddle_factor - 1.f) * |
| dist_between_off_plane_points * |
| plane.dir(); |
| |
| // Finally, let's intersect some points with the plane. |
| auto result = TestPlaneIntersection(plane, pt1, pt2); |
| EXPECT_NE(result, FLT_MAX); |
| EXPECT_LE(result, 1.f); |
| EXPECT_GE(result, 0.f); |
| vec3 intersection_point = pt1 + result * (pt2 - pt1); |
| |
| EXPECT_LT(glm::length(point_on_plane - intersection_point), 1.f); |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| TEST(plane2, NonIntersection) { |
| vec2 point_on_plane = vec2(40, 30); |
| vec2 offset_vec = vec2(100, 20); |
| plane2 plane(point_on_plane, glm::normalize(offset_vec)); |
| |
| // Rotate |offset_vec| by 90 degrees. |
| vec2 parallel_vec(-offset_vec.y, offset_vec.x); |
| |
| // Starting from a point known to not be on the plane, verify that the |
| // parallel ray does not intersect the plane. |
| vec2 pt2(vec2(30, -40)); |
| auto result = TestPlaneIntersection(plane, pt2, pt2 + parallel_vec); |
| EXPECT_EQ(result, FLT_MAX); |
| |
| // Perturb the ray direction slightly; it should now intersect the plane. |
| vec2 non_parallel_vec = parallel_vec + vec2(0, .1f); |
| result = TestPlaneIntersection(plane, pt2, pt2 + non_parallel_vec); |
| EXPECT_NE(result, FLT_MAX); |
| |
| // Compute the intersection point. Since the ray and plane are nearly |
| // parallel, the precision will not be high. Still, relative to the magnitude |
| // of the intersection point, it's not bad. |
| vec2 intersection_point = pt2 + result * non_parallel_vec; |
| EXPECT_NEAR(glm::dot(plane.dir(), intersection_point), plane.dist(), |
| glm::length(intersection_point) / 10000000.f); |
| } |
| |
| // Helper function for TEST(plane3, Transformation). |
| template <typename PlaneT> |
| void TestPlaneTransformation(const Transform& transform, |
| const std::vector<PlaneT>& planes) { |
| using VecT = typename PlaneT::VectorType; |
| |
| // The planes start in world-space, and are transformed into object-space. |
| mat4 matrix = static_cast<mat4>(transform); |
| std::vector<PlaneT> output_planes; |
| for (auto& p : planes) { |
| output_planes.push_back(TransformPlane(matrix, p)); |
| } |
| |
| // Synthesize a grid of points in object-space and verify that their |
| // distances from the object-space plane are the same as transforming them |
| // into world-space and testing against the world-space plane. |
| for (float pt_x = -17.5f; pt_x < 20.f; pt_x += 5.f) { |
| for (float pt_y = -17.5f; pt_y < 20.f; pt_y += 5.f) { |
| for (float pt_z = -17.5f; pt_z < 20.f; pt_z += 5.f) { |
| const VecT object_space_point(vec3(pt_x, pt_y, pt_z)); |
| const VecT world_space_point(matrix * Homo4(object_space_point, 1)); |
| |
| for (size_t i = 0; i < planes.size(); ++i) { |
| const PlaneT& world_space_plane = planes[i]; |
| const PlaneT& object_space_plane = output_planes[i]; |
| |
| const float world_space_distance = |
| PlaneDistanceToPoint(world_space_plane, world_space_point); |
| const float object_space_distance = |
| PlaneDistanceToPoint(object_space_plane, object_space_point); |
| const float object_space_distance_scaled = |
| object_space_distance * transform.scale.x; |
| |
| const float kFudgedEpsilon = kEpsilon * 1000.f; |
| EXPECT_NEAR(world_space_distance, object_space_distance_scaled, |
| kFudgedEpsilon); |
| } |
| } |
| } |
| } |
| } |
| |
| // Test matrix transformation of world-space planes into object-space. |
| TEST(plane3, Transformation) { |
| // Choose some arbtrary planes to transform. |
| std::vector<plane3> planes3( |
| {plane3(glm::normalize(vec3(1, 1, 1)), -5.f), |
| plane3(glm::normalize(vec3(1, 1, 1)), 5.f), |
| plane3(glm::normalize(vec3(-1, 10, 100)), -15.f), |
| plane3(glm::normalize(vec3(1, -10, -100)), -15.f)}); |
| |
| // To test plane2 in addition to plane3, we drop the z-coordinate and then |
| // renormalize. |
| std::vector<plane2> planes2; |
| for (auto& p : planes3) { |
| planes2.push_back(plane2(glm::normalize(vec2(p.dir())), p.dist())); |
| } |
| |
| // Step through parameter-space to generate a large number of Transforms. |
| for (float trans_x = -220.f; trans_x <= 220.f; trans_x += 110.f) { |
| for (float trans_y = -220.f; trans_y <= 220.f; trans_y += 110.f) { |
| for (float trans_z = -220.f; trans_z <= 220.f; trans_z += 110.f) { |
| for (float scale = 0.5f; scale <= 4.f; scale *= 2.f) { |
| for (float angle = 0.f; angle < M_PI; angle += M_PI / 2.9f) { |
| // For 2D, test by rotating around Z-axis. |
| TestPlaneTransformation( |
| Transform(vec3(trans_x, trans_y, trans_z), |
| vec3(scale, scale, scale), |
| glm::angleAxis(angle, vec3(0, 0, 1))), |
| planes2); |
| |
| // For 3D, test by rotating off the Z-axis. |
| TestPlaneTransformation( |
| Transform( |
| vec3(trans_x, trans_y, trans_z), vec3(scale, scale, scale), |
| glm::angleAxis(angle, glm::normalize(vec3(0, .4f, 1)))), |
| planes3); |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| // Test that we get the same behavior when transforming a plane into |
| // object-space via a translation vector, as with an equivalent matrix. |
| TEST(plane3, Translation) { |
| std::vector<plane3> planes({ |
| plane3(glm::normalize(vec3(1, 0, 0)), 5.f), |
| plane3(glm::normalize(vec3(1, 1, 1)), -5.f), |
| plane3(glm::normalize(vec3(1, 1, 1)), 5.f), |
| plane3(glm::normalize(vec3(-1, 10, 100)), -15.f), |
| plane3(glm::normalize(vec3(1, -10, -100)), -15.f), |
| }); |
| |
| std::vector<vec3> translations({vec3(30, 40, 50), vec3(30, 40, -50), |
| vec3(30, -40, 50), vec3(-30, 40, 50)}); |
| |
| for (auto& trans : translations) { |
| mat4 trans_matrix = glm::translate(mat4(), trans); |
| |
| for (size_t i = 0; i < planes.size(); ++i) { |
| plane3& world_space_plane = planes[i]; |
| plane3 translated_object_space_plane = TranslatePlane(trans, planes[i]); |
| plane3 transformed_object_space_plane = |
| TransformPlane(trans_matrix, planes[i]); |
| |
| // Compute a 3D grid of object-space points, in order to compare them |
| // against the world-space and object-space planes. |
| for (float pt_x = 35.f; pt_x < 40.f; pt_x += 10.f) { |
| for (float pt_y = 35.f; pt_y < 40.f; pt_y += 10.f) { |
| for (float pt_z = 35.f; pt_z < 40.f; pt_z += 10.f) { |
| vec3 object_space_point(pt_x, pt_y, pt_z); |
| vec3 world_space_point = object_space_point + trans; |
| |
| // Verify that the world-space point/plane distance matches the |
| // object-space distances, regardless of whether the translation was |
| // specified by a vector or a matrix. |
| const float world_space_distance = |
| PlaneDistanceToPoint(world_space_plane, world_space_point); |
| const float object_space_distance_1 = PlaneDistanceToPoint( |
| translated_object_space_plane, object_space_point); |
| const float object_space_distance_2 = PlaneDistanceToPoint( |
| transformed_object_space_plane, object_space_point); |
| |
| // In many cases kEpsilon is sufficient, but in others there is less |
| // precision. |
| const float kFudgedEpsilon = kEpsilon * 100; |
| EXPECT_NEAR(world_space_distance, object_space_distance_1, |
| kFudgedEpsilon); |
| EXPECT_NEAR(world_space_distance, object_space_distance_2, |
| kFudgedEpsilon); |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| // Test that we get the same behavior when transforming a plane into |
| // object-space via a uniform scale factor, as with an equivalent matrix. |
| TEST(plane3, UniformScale) { |
| std::vector<plane3> planes({ |
| plane3(glm::normalize(vec3(1, 0, 0)), 5.f), |
| plane3(glm::normalize(vec3(1, 1, 1)), -5.f), |
| plane3(glm::normalize(vec3(1, 1, 1)), 5.f), |
| plane3(glm::normalize(vec3(-1, 10, 100)), -15.f), |
| plane3(glm::normalize(vec3(1, -10, -100)), -15.f), |
| }); |
| |
| std::vector<float> scales({0.3f, 0.8f, 1.4f, 8.7f}); |
| |
| for (auto& scale : scales) { |
| mat4 scale_matrix = glm::scale(mat4(), vec3(scale, scale, scale)); |
| |
| for (size_t i = 0; i < planes.size(); ++i) { |
| plane3& world_space_plane = planes[i]; |
| plane3 scaled_object_space_plane = ScalePlane(scale, planes[i]); |
| plane3 transformed_object_space_plane = |
| TransformPlane(scale_matrix, planes[i]); |
| |
| // Compute a 3D grid of object-space points, in order to compare them |
| // against the world-space and object-space planes. |
| for (float pt_x = 35.f; pt_x < 40.f; pt_x += 10.f) { |
| for (float pt_y = 35.f; pt_y < 40.f; pt_y += 10.f) { |
| for (float pt_z = 35.f; pt_z < 40.f; pt_z += 10.f) { |
| vec3 object_space_point(pt_x, pt_y, pt_z); |
| vec3 world_space_point = scale * object_space_point; |
| |
| // Verify that the world-space point/plane distance matches the |
| // object-space distances, regardless of whether the scale was |
| // specified by a scalar or a matrix. |
| const float world_space_distance = |
| PlaneDistanceToPoint(world_space_plane, world_space_point); |
| const float object_space_distance_1 = PlaneDistanceToPoint( |
| scaled_object_space_plane, object_space_point); |
| const float object_space_distance_2 = PlaneDistanceToPoint( |
| transformed_object_space_plane, object_space_point); |
| |
| // In many cases kEpsilon is sufficient, but in others there is |
| // less precision. |
| const float kFudgedEpsilon = kEpsilon * 100; |
| |
| // We first need to scale the object-space distances in order to |
| // compare them to the world-space distance. |
| EXPECT_NEAR(world_space_distance, object_space_distance_1 * scale, |
| kFudgedEpsilon); |
| EXPECT_NEAR(world_space_distance, object_space_distance_2 * scale, |
| kFudgedEpsilon); |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| } // namespace |
