283 lines
10 KiB
C++
283 lines
10 KiB
C++
#include <mbgl/util/bounding_volumes.hpp>
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#include <algorithm>
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#include <cassert>
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#include <cmath>
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namespace mbgl {
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namespace {
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vec3 toVec3(const vec4& v) {
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return vec3{v[0], v[1], v[2]};
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}
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vec3 vec3Sub(const vec3& a, const vec3& b) {
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return vec3{a[0] - b[0], a[1] - b[1], a[2] - b[2]};
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}
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vec3 vec3Scale(const vec3& a, double s) {
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return vec3{a[0] * s, a[1] * s, a[2] * s};
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}
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vec3 vec3Cross(const vec3& a, const vec3& b) {
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return vec3{a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]};
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}
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double vec3Dot(const vec3& a, const vec3& b) {
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return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
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}
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double vec3LengthSq(const vec3& a) {
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return vec3Dot(a, a);
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}
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double vec3Length(const vec3& a) {
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return std::sqrt(vec3LengthSq(a));
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}
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vec3 vec3Normalize(const vec3& a) {
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return vec3Scale(a, 1.0 / vec3Length(a));
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}
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double vec4Dot(const vec4& a, const vec4& b) {
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return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
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}
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template <size_t N>
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static Point<double> ProjectPointsToAxis(const std::array<vec3, N>& points, const vec3& origin, const vec3& axis) {
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double min = std::numeric_limits<double>::max();
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double max = -std::numeric_limits<double>::max();
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for (const vec3& point : points) {
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double projectedPoint = vec3Dot(vec3Sub(point, origin), axis);
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min = std::min(projectedPoint, min);
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max = std::max(projectedPoint, max);
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}
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return {min, max};
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}
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} // namespace
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namespace util {
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AABB::AABB() : min({0, 0, 0}), max({0, 0, 0}) {}
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AABB::AABB(const vec3& min_, const vec3& max_) : min(min_), max(max_) {}
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vec3 AABB::closestPoint(const vec3& point) const {
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return {std::max(std::min(max[0], point[0]), min[0]),
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std::max(std::min(max[1], point[1]), min[1]),
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std::max(std::min(max[2], point[2]), min[2])};
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}
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vec3 AABB::distanceXYZ(const vec3& point) const {
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vec3 vec = vec3Sub(closestPoint(point), point);
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vec[0] = std::abs(vec[0]);
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vec[1] = std::abs(vec[1]);
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vec[2] = std::abs(vec[2]);
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return vec;
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}
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AABB AABB::quadrant(int idx) const {
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assert(idx >= 0 && idx < 4);
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vec3 quadrantMin = min;
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vec3 quadrantMax = max;
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const double xCenter = 0.5 * (max[0] + min[0]);
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const double yCenter = 0.5 * (max[1] + min[1]);
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// This aabb is split into 4 quadrants. For each axis define in which side of the split "idx" is
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// The result for indices 0, 1, 2, 3 is: { 0, 0 }, { 1, 0 }, { 0, 1 }, { 1, 1 }
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const std::array<int, 4> xSplit = {0, 1, 0, 1};
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const std::array<int, 4> ySplit = {0, 0, 1, 1};
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quadrantMin[0] = xSplit[idx] ? xCenter : quadrantMin[0];
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quadrantMax[0] = xSplit[idx] ? quadrantMax[0] : xCenter;
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quadrantMin[1] = ySplit[idx] ? yCenter : quadrantMin[1];
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quadrantMax[1] = ySplit[idx] ? quadrantMax[1] : yCenter;
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return {quadrantMin, quadrantMax};
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}
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bool AABB::intersects(const AABB& aabb) const {
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if (min[0] > aabb.max[0] || aabb.min[0] > max[0]) return false;
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if (min[1] > aabb.max[1] || aabb.min[1] > max[1]) return false;
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if (min[2] > aabb.max[2] || aabb.min[2] > max[2]) return false;
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return true;
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}
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bool AABB::operator==(const AABB& aabb) const {
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return min == aabb.min && max == aabb.max;
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}
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bool AABB::operator!=(const AABB& aabb) const {
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return !(*this == aabb);
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}
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// Named index values for frustum::points array
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enum {
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near_tl = 0,
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near_tr = 1,
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near_br = 2,
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near_bl = 3,
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far_tl = 4,
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far_tr = 5,
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far_br = 6,
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far_bl = 7,
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};
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Frustum::Frustum(const std::array<vec3, 8>& points_, const std::array<vec4, 6>& planes_)
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: points(points_), planes(planes_) {
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const Point<double> xBounds = ProjectPointsToAxis(points, {0, 0, 0}, {1, 0, 0});
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const Point<double> yBounds = ProjectPointsToAxis(points, {0, 0, 0}, {0, 1, 0});
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const Point<double> zBounds = ProjectPointsToAxis(points, {0, 0, 0}, {0, 0, 1});
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bounds = AABB({xBounds.x, yBounds.x, zBounds.x}, {xBounds.y, yBounds.y, zBounds.y});
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// Precompute a set of separating axis candidates for precise intersection tests.
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// Remaining axes not covered in basic intersection tests are: axis[] = (edges of aabb) x (edges of frustum)
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std::array<vec3, 6> frustumEdges = {vec3Sub(points[near_br], points[near_bl]),
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vec3Sub(points[near_tl], points[near_bl]),
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vec3Sub(points[far_tl], points[near_tl]),
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vec3Sub(points[far_tr], points[near_tr]),
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vec3Sub(points[far_br], points[near_br]),
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vec3Sub(points[far_bl], points[near_bl])};
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for (size_t i = 0; i < frustumEdges.size(); i++) {
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// Cross product [1, 0, 0] x [a, b, c] == [0, -c, b]
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// Cross product [0, 1, 0] x [a, b, c] == [c, 0, -a]
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const vec3 axis0 = {0.0, -frustumEdges[i][2], frustumEdges[i][1]};
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const vec3 axis1 = {frustumEdges[i][2], 0.0, -frustumEdges[i][0]};
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projections[i * 2] = {axis0, ProjectPointsToAxis(points, points[0], axis0)};
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projections[i * 2 + 1] = {axis1, ProjectPointsToAxis(points, points[0], axis1)};
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}
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}
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Frustum Frustum::fromInvProjMatrix(const mat4& invProj, double worldSize, double zoom, bool flippedY) {
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// Define frustum corner points in normalized clip space
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std::array<vec4, 8> cornerCoords = {vec4{-1.0, 1.0, -1.0, 1.0},
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vec4{1.0, 1.0, -1.0, 1.0},
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vec4{1.0, -1.0, -1.0, 1.0},
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vec4{-1.0, -1.0, -1.0, 1.0},
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vec4{-1.0, 1.0, 1.0, 1.0},
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vec4{1.0, 1.0, 1.0, 1.0},
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vec4{1.0, -1.0, 1.0, 1.0},
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vec4{-1.0, -1.0, 1.0, 1.0}};
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const double scale = std::pow(2.0, zoom);
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// Transform points to tile space
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for (auto& coord : cornerCoords) {
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matrix::transformMat4(coord, coord, invProj);
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for (auto& component : coord) component *= 1.0 / coord[3] / worldSize * scale;
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}
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std::array<vec3i, 6> frustumPlanePointIndices = {
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vec3i{near_bl, near_br, far_br}, // bottom
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vec3i{near_tl, near_bl, far_bl}, // left
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vec3i{near_br, near_tr, far_tr}, // right
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vec3i{near_tl, far_tl, far_tr}, // top
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vec3i{near_tl, near_tr, near_br}, // near
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vec3i{far_br, far_tr, far_tl} // far
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};
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if (flippedY) {
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std::for_each(frustumPlanePointIndices.begin(), frustumPlanePointIndices.end(), [](vec3i& tri) {
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std::swap(tri[1], tri[2]);
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});
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}
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std::array<vec4, 6> frustumPlanes;
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for (std::size_t i = 0; i < frustumPlanePointIndices.size(); i++) {
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const vec3i indices = frustumPlanePointIndices[i];
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// Compute plane equation using 3 points on the plane
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const vec3 p0 = toVec3(cornerCoords[indices[0]]);
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const vec3 p1 = toVec3(cornerCoords[indices[1]]);
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const vec3 p2 = toVec3(cornerCoords[indices[2]]);
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const vec3 a = vec3Sub(p0, p1);
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const vec3 b = vec3Sub(p2, p1);
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const vec3 n = vec3Normalize(vec3Cross(a, b));
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frustumPlanes[i] = {n[0], n[1], n[2], -vec3Dot(n, p1)};
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}
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std::array<vec3, 8> frustumPoints;
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for (size_t i = 0; i < cornerCoords.size(); i++) frustumPoints[i] = toVec3(cornerCoords[i]);
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return {frustumPoints, frustumPlanes};
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}
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IntersectionResult Frustum::intersects(const AABB& aabb) const {
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// Execute separating axis test between two convex objects to find intersections
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// Each frustum plane together with 3 major axes define the separating axes
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// This implementation is conservative as it's not checking all possible axes.
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// False positive rate is ~0.5% of all cases (see intersectsPrecise).
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// Note: test only 4 points as both min and max points have zero elevation
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assert(aabb.min[2] == 0.0 && aabb.max[2] == 0.0);
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if (!bounds.intersects(aabb)) return IntersectionResult::Separate;
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const std::array<vec4, 4> aabbPoints = {
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vec4{aabb.min[0], aabb.min[1], 0.0, 1.0},
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vec4{aabb.max[0], aabb.min[1], 0.0, 1.0},
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vec4{aabb.max[0], aabb.max[1], 0.0, 1.0},
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vec4{aabb.min[0], aabb.max[1], 0.0, 1.0},
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};
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bool fullyInside = true;
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for (const vec4& plane : planes) {
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size_t pointsInside = 0;
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pointsInside += vec4Dot(plane, aabbPoints[0]) >= 0.0;
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pointsInside += vec4Dot(plane, aabbPoints[1]) >= 0.0;
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pointsInside += vec4Dot(plane, aabbPoints[2]) >= 0.0;
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pointsInside += vec4Dot(plane, aabbPoints[3]) >= 0.0;
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if (!pointsInside) {
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// Separating axis found, no intersection
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return IntersectionResult::Separate;
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}
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if (pointsInside != aabbPoints.size()) fullyInside = false;
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}
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return fullyInside ? IntersectionResult::Contains : IntersectionResult::Intersects;
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}
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IntersectionResult Frustum::intersectsPrecise(const AABB& aabb, bool edgeCasesOnly) const {
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if (!edgeCasesOnly) {
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IntersectionResult result = intersects(aabb);
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if (result == IntersectionResult::Separate) return result;
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}
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const std::array<vec3, 4> aabbPoints = {vec3{aabb.min[0], aabb.min[1], 0.0},
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vec3{aabb.max[0], aabb.min[1], 0.0},
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vec3{aabb.max[0], aabb.max[1], 0.0},
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vec3{aabb.min[0], aabb.max[1], 0.0}};
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// For a precise SAT-test all edge cases needs to be covered
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// Projections of the frustum on separating axis candidates have been precomputed already
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for (const Projection& proj : projections) {
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Point<double> projectedAabb = ProjectPointsToAxis(aabbPoints, points[0], proj.axis);
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const Point<double>& projectedFrustum = proj.projection;
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if (projectedFrustum.y < projectedAabb.x || projectedFrustum.x > projectedAabb.y) {
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return IntersectionResult::Separate;
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}
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}
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return IntersectionResult::Intersects;
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}
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} // namespace util
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} // namespace mbgl
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