Refactor tileCover to support lod tiles

1 files changed, 283 insertions, 0 deletions

diff --git a/src/mbgl/util/bounding_volumes.cpp b/src/mbgl/util/bounding_volumes.cpp
new file mode 100644
index 0000000000..8d34f9bd62
--- /dev/null
+++ b/src/mbgl/util/bounding_volumes.cpp
@@ -0,0 +1,283 @@
+#include <mbgl/util/bounding_volumes.hpp>
+
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+
+namespace mbgl {
+namespace {
+
+vec3 toVec3(const vec4& v) {
+    return vec3{v[0], v[1], v[2]};
+}
+
+vec3 vec3Sub(const vec3& a, const vec3& b) {
+    return vec3{a[0] - b[0], a[1] - b[1], a[2] - b[2]};
+}
+
+vec3 vec3Scale(const vec3& a, double s) {
+    return vec3{a[0] * s, a[1] * s, a[2] * s};
+}
+
+vec3 vec3Cross(const vec3& a, const vec3& b) {
+    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]};
+}
+
+double vec3Dot(const vec3& a, const vec3& b) {
+    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+}
+
+double vec3LengthSq(const vec3& a) {
+    return vec3Dot(a, a);
+}
+
+double vec3Length(const vec3& a) {
+    return std::sqrt(vec3LengthSq(a));
+}
+
+vec3 vec3Normalize(const vec3& a) {
+    return vec3Scale(a, 1.0 / vec3Length(a));
+}
+
+double vec4Dot(const vec4& a, const vec4& b) {
+    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
+}
+
+template <size_t N>
+static Point<double> ProjectPointsToAxis(const std::array<vec3, N>& points, const vec3& origin, const vec3& axis) {
+    double min = std::numeric_limits<double>::max();
+    double max = -std::numeric_limits<double>::max();
+
+    for (const vec3& point : points) {
+        double projectedPoint = vec3Dot(vec3Sub(point, origin), axis);
+        min = std::min(projectedPoint, min);
+        max = std::max(projectedPoint, max);
+    }
+
+    return {min, max};
+}
+
+} // namespace
+
+namespace util {
+
+AABB::AABB() : min({0, 0, 0}), max({0, 0, 0}) {}
+
+AABB::AABB(const vec3& min_, const vec3& max_) : min(min_), max(max_) {}
+
+vec3 AABB::closestPoint(const vec3& point) const {
+    return {std::max(std::min(max[0], point[0]), min[0]),
+            std::max(std::min(max[1], point[1]), min[1]),
+            std::max(std::min(max[2], point[2]), min[2])};
+}
+
+vec3 AABB::distanceXYZ(const vec3& point) const {
+    vec3 vec = vec3Sub(closestPoint(point), point);
+
+    vec[0] = std::abs(vec[0]);
+    vec[1] = std::abs(vec[1]);
+    vec[2] = std::abs(vec[2]);
+
+    return vec;
+}
+
+AABB AABB::quadrant(int idx) const {
+    assert(idx >= 0 && idx < 4);
+    vec3 quadrantMin = min;
+    vec3 quadrantMax = max;
+    const double xCenter = 0.5 * (max[0] + min[0]);
+    const double yCenter = 0.5 * (max[1] + min[1]);
+
+    // This aabb is split into 4 quadrants. For each axis define in which side of the split "idx" is
+    // The result for indices 0, 1, 2, 3 is: { 0, 0 }, { 1, 0 }, { 0, 1 }, { 1, 1 }
+    const std::array<int, 4> xSplit = {0, 1, 0, 1};
+    const std::array<int, 4> ySplit = {0, 0, 1, 1};
+
+    quadrantMin[0] = xSplit[idx] ? xCenter : quadrantMin[0];
+    quadrantMax[0] = xSplit[idx] ? quadrantMax[0] : xCenter;
+
+    quadrantMin[1] = ySplit[idx] ? yCenter : quadrantMin[1];
+    quadrantMax[1] = ySplit[idx] ? quadrantMax[1] : yCenter;
+
+    return {quadrantMin, quadrantMax};
+}
+
+bool AABB::intersects(const AABB& aabb) const {
+    if (min[0] > aabb.max[0] || aabb.min[0] > max[0]) return false;
+    if (min[1] > aabb.max[1] || aabb.min[1] > max[1]) return false;
+    if (min[2] > aabb.max[2] || aabb.min[2] > max[2]) return false;
+    return true;
+}
+
+bool AABB::operator==(const AABB& aabb) const {
+    return min == aabb.min && max == aabb.max;
+}
+
+bool AABB::operator!=(const AABB& aabb) const {
+    return !(*this == aabb);
+}
+
+// Named index values for frustum::points array
+enum {
+    near_tl = 0,
+    near_tr = 1,
+    near_br = 2,
+    near_bl = 3,
+    far_tl = 4,
+    far_tr = 5,
+    far_br = 6,
+    far_bl = 7,
+};
+
+Frustum::Frustum(const std::array<vec3, 8>& points_, const std::array<vec4, 6>& planes_)
+    : points(points_), planes(planes_) {
+    const Point<double> xBounds = ProjectPointsToAxis(points, {0, 0, 0}, {1, 0, 0});
+    const Point<double> yBounds = ProjectPointsToAxis(points, {0, 0, 0}, {0, 1, 0});
+    const Point<double> zBounds = ProjectPointsToAxis(points, {0, 0, 0}, {0, 0, 1});
+
+    bounds = AABB({xBounds.x, yBounds.x, zBounds.x}, {xBounds.y, yBounds.y, zBounds.y});
+
+    // Precompute a set of separating axis candidates for precise intersection tests.
+    // Remaining axes not covered in basic intersection tests are: axis[] = (edges of aabb) x (edges of frustum)
+    std::array<vec3, 6> frustumEdges = {vec3Sub(points[near_br], points[near_bl]),
+                                        vec3Sub(points[near_tl], points[near_bl]),
+                                        vec3Sub(points[far_tl], points[near_tl]),
+                                        vec3Sub(points[far_tr], points[near_tr]),
+                                        vec3Sub(points[far_br], points[near_br]),
+                                        vec3Sub(points[far_bl], points[near_bl])};
+
+    for (size_t i = 0; i < frustumEdges.size(); i++) {
+        // Cross product [1, 0, 0] x [a, b, c] == [0, -c, b]
+        // Cross product [0, 1, 0] x [a, b, c] == [c, 0, -a]
+        const vec3 axis0 = {0.0, -frustumEdges[i][2], frustumEdges[i][1]};
+        const vec3 axis1 = {frustumEdges[i][2], 0.0, -frustumEdges[i][0]};
+
+        projections[i * 2] = {axis0, ProjectPointsToAxis(points, points[0], axis0)};
+        projections[i * 2 + 1] = {axis1, ProjectPointsToAxis(points, points[0], axis1)};
+    }
+}
+
+Frustum Frustum::fromInvProjMatrix(const mat4& invProj, double worldSize, double zoom, bool flippedY) {
+    // Define frustum corner points in normalized clip space
+    std::array<vec4, 8> cornerCoords = {vec4{-1.0, 1.0, -1.0, 1.0},
+                                        vec4{1.0, 1.0, -1.0, 1.0},
+                                        vec4{1.0, -1.0, -1.0, 1.0},
+                                        vec4{-1.0, -1.0, -1.0, 1.0},
+                                        vec4{-1.0, 1.0, 1.0, 1.0},
+                                        vec4{1.0, 1.0, 1.0, 1.0},
+                                        vec4{1.0, -1.0, 1.0, 1.0},
+                                        vec4{-1.0, -1.0, 1.0, 1.0}};
+
+    const double scale = std::pow(2.0, zoom);
+
+    // Transform points to tile space
+    for (auto& coord : cornerCoords) {
+        matrix::transformMat4(coord, coord, invProj);
+        for (auto& component : coord) component *= 1.0 / coord[3] / worldSize * scale;
+    }
+
+    std::array<vec3i, 6> frustumPlanePointIndices = {
+        vec3i{near_bl, near_br, far_br},  // bottom
+        vec3i{near_tl, near_bl, far_bl},  // left
+        vec3i{near_br, near_tr, far_tr},  // right
+        vec3i{near_tl, far_tl, far_tr},   // top
+        vec3i{near_tl, near_tr, near_br}, // near
+        vec3i{far_br, far_tr, far_tl}     // far
+    };
+
+    if (flippedY) {
+        std::for_each(frustumPlanePointIndices.begin(), frustumPlanePointIndices.end(), [](vec3i& tri) {
+            std::swap(tri[1], tri[2]);
+        });
+    }
+
+    std::array<vec4, 6> frustumPlanes;
+
+    for (std::size_t i = 0; i < frustumPlanePointIndices.size(); i++) {
+        const vec3i indices = frustumPlanePointIndices[i];
+
+        // Compute plane equation using 3 points on the plane
+        const vec3 p0 = toVec3(cornerCoords[indices[0]]);
+        const vec3 p1 = toVec3(cornerCoords[indices[1]]);
+        const vec3 p2 = toVec3(cornerCoords[indices[2]]);
+
+        const vec3 a = vec3Sub(p0, p1);
+        const vec3 b = vec3Sub(p2, p1);
+        const vec3 n = vec3Normalize(vec3Cross(a, b));
+
+        frustumPlanes[i] = {n[0], n[1], n[2], -vec3Dot(n, p1)};
+    }
+
+    std::array<vec3, 8> frustumPoints;
+
+    for (size_t i = 0; i < cornerCoords.size(); i++) frustumPoints[i] = toVec3(cornerCoords[i]);
+
+    return {frustumPoints, frustumPlanes};
+}
+
+IntersectionResult Frustum::intersects(const AABB& aabb) const {
+    // Execute separating axis test between two convex objects to find intersections
+    // Each frustum plane together with 3 major axes define the separating axes
+    // This implementation is conservative as it's not checking all possible axes.
+    // False positive rate is ~0.5% of all cases (see intersectsPrecise).
+    // Note: test only 4 points as both min and max points have zero elevation
+    assert(aabb.min[2] == 0.0 && aabb.max[2] == 0.0);
+
+    if (!bounds.intersects(aabb)) return IntersectionResult::Separate;
+
+    const std::array<vec4, 4> aabbPoints = {
+        vec4{aabb.min[0], aabb.min[1], 0.0, 1.0},
+        vec4{aabb.max[0], aabb.min[1], 0.0, 1.0},
+        vec4{aabb.max[0], aabb.max[1], 0.0, 1.0},
+        vec4{aabb.min[0], aabb.max[1], 0.0, 1.0},
+    };
+
+    bool fullyInside = true;
+
+    for (const vec4& plane : planes) {
+        size_t pointsInside = 0;
+
+        pointsInside += vec4Dot(plane, aabbPoints[0]) >= 0.0;
+        pointsInside += vec4Dot(plane, aabbPoints[1]) >= 0.0;
+        pointsInside += vec4Dot(plane, aabbPoints[2]) >= 0.0;
+        pointsInside += vec4Dot(plane, aabbPoints[3]) >= 0.0;
+
+        if (!pointsInside) {
+            // Separating axis found, no intersection
+            return IntersectionResult::Separate;
+        }
+
+        if (pointsInside != aabbPoints.size()) fullyInside = false;
+    }
+
+    return fullyInside ? IntersectionResult::Contains : IntersectionResult::Intersects;
+}
+
+IntersectionResult Frustum::intersectsPrecise(const AABB& aabb, bool edgeCasesOnly) const {
+    if (!edgeCasesOnly) {
+        IntersectionResult result = intersects(aabb);
+
+        if (result == IntersectionResult::Separate) return result;
+    }
+
+    const std::array<vec3, 4> aabbPoints = {vec3{aabb.min[0], aabb.min[1], 0.0},
+                                            vec3{aabb.max[0], aabb.min[1], 0.0},
+                                            vec3{aabb.max[0], aabb.max[1], 0.0},
+                                            vec3{aabb.min[0], aabb.max[1], 0.0}};
+
+    // For a precise SAT-test all edge cases needs to be covered
+    // Projections of the frustum on separating axis candidates have been precomputed already
+    for (const Projection& proj : projections) {
+        Point<double> projectedAabb = ProjectPointsToAxis(aabbPoints, points[0], proj.axis);
+        const Point<double>& projectedFrustum = proj.projection;
+
+        if (projectedFrustum.y < projectedAabb.x || projectedFrustum.x > projectedAabb.y) {
+            return IntersectionResult::Separate;
+        }
+    }
+
+    return IntersectionResult::Intersects;
+}
+
+} // namespace util
+} // namespace mbgl
\ No newline at end of file