// //--------------------------------------------------------------------------- // AABB-tree used for ray testing // Copyright(C) 2017 Magnus Norddahl // All rights reserved. // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU Lesser General Public License as published by // the Free Software Foundation, either version 2 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU Lesser General Public License for more details. // // You should have received a copy of the GNU Lesser General Public License // along with this program. If not, see http://www.gnu.org/licenses/ // //-------------------------------------------------------------------------- // #include #include "hw_aabbtree.h" namespace hwrenderer { TArray LevelAABBTree::FindNodePath(unsigned int line, unsigned int node) { const AABBTreeNode &n = nodes[node]; if (n.aabb_left > treelines[line].x || n.aabb_right < treelines[line].x || n.aabb_top > treelines[line].y || n.aabb_bottom < treelines[line].y) { return {}; } TArray path; if (n.line_index == -1) { path = FindNodePath(line, n.left_node); if (path.Size() == 0) path = FindNodePath(line, n.right_node); if (path.Size()) path.Push(node); } else if (n.line_index == (int)line) { path.Push(node); } return path; } double LevelAABBTree::RayTest(const DVector3 &ray_start, const DVector3 &ray_end) { // Precalculate some of the variables used by the ray/line intersection test DVector2 raydelta = ray_end - ray_start; double raydist2 = raydelta | raydelta; DVector2 raynormal = DVector2(raydelta.Y, -raydelta.X); double rayd = raynormal | ray_start; if (raydist2 < 1.0) return 1.0f; double hit_fraction = 1.0; // Walk the tree nodes int stack[32]; int stack_pos = 1; stack[0] = nodes.Size() - 1; // root node is the last node in the list while (stack_pos > 0) { int node_index = stack[stack_pos - 1]; if (!OverlapRayAABB(ray_start, ray_end, nodes[node_index])) { // If the ray doesn't overlap this node's AABB we're done for this subtree stack_pos--; } else if (nodes[node_index].line_index != -1) // isLeaf(node_index) { // We reached a leaf node. Do a ray/line intersection test to see if we hit the line. hit_fraction = std::min(IntersectRayLine(ray_start, ray_end, nodes[node_index].line_index, raydelta, rayd, raydist2), hit_fraction); stack_pos--; } else if (stack_pos == 32) { stack_pos--; // stack overflow - tree is too deep! } else { // The ray overlaps the node's AABB. Examine its child nodes. stack[stack_pos - 1] = nodes[node_index].left_node; stack[stack_pos] = nodes[node_index].right_node; stack_pos++; } } return hit_fraction; } bool LevelAABBTree::OverlapRayAABB(const DVector2 &ray_start2d, const DVector2 &ray_end2d, const AABBTreeNode &node) { // To do: simplify test to use a 2D test DVector3 ray_start = DVector3(ray_start2d, 0.0); DVector3 ray_end = DVector3(ray_end2d, 0.0); DVector3 aabb_min = DVector3(node.aabb_left, node.aabb_top, -1.0); DVector3 aabb_max = DVector3(node.aabb_right, node.aabb_bottom, 1.0); // Standard 3D ray/AABB overlapping test. // The details for the math here can be found in Real-Time Rendering, 3rd Edition. // We could use a 2D test here instead, which would probably simplify the math. DVector3 c = (ray_start + ray_end) * 0.5f; DVector3 w = ray_end - c; DVector3 h = (aabb_max - aabb_min) * 0.5f; // aabb.extents(); c -= (aabb_max + aabb_min) * 0.5f; // aabb.center(); DVector3 v = DVector3(fabs(w.X), fabs(w.Y), fabs(w.Z)); if (fabs(c.X) > v.X + h.X || fabs(c.Y) > v.Y + h.Y || fabs(c.Z) > v.Z + h.Z) return false; // disjoint; if (fabs(c.Y * w.Z - c.Z * w.Y) > h.Y * v.Z + h.Z * v.Y || fabs(c.X * w.Z - c.Z * w.X) > h.X * v.Z + h.Z * v.X || fabs(c.X * w.Y - c.Y * w.X) > h.X * v.Y + h.Y * v.X) return false; // disjoint; return true; // overlap; } double LevelAABBTree::IntersectRayLine(const DVector2 &ray_start, const DVector2 &ray_end, int line_index, const DVector2 &raydelta, double rayd, double raydist2) { // Check if two line segments intersects (the ray and the line). // The math below does this by first finding the fractional hit for an infinitely long ray line. // If that hit is within the line segment (0 to 1 range) then it calculates the fractional hit for where the ray would hit. // // This algorithm is homemade - I would not be surprised if there's a much faster method out there. const double epsilon = 0.0000001; const AABBTreeLine &line = treelines[line_index]; DVector2 raynormal = DVector2(raydelta.Y, -raydelta.X); DVector2 line_pos(line.x, line.y); DVector2 line_delta(line.dx, line.dy); double den = raynormal | line_delta; if (fabs(den) > epsilon) { double t_line = (rayd - (raynormal | line_pos)) / den; if (t_line >= 0.0 && t_line <= 1.0) { DVector2 linehitdelta = line_pos + line_delta * t_line - ray_start; double t = (raydelta | linehitdelta) / raydist2; return t > 0.0 ? t : 1.0; } } return 1.0; } }