174 lines
6.6 KiB
HLSL
174 lines
6.6 KiB
HLSL
#ifndef UNITY_GEOMETRICTOOLS_INCLUDED
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#define UNITY_GEOMETRICTOOLS_INCLUDED
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//-----------------------------------------------------------------------------
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// Intersection functions
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//-----------------------------------------------------------------------------
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// return furthest near intersection in x and closest far intersection in y
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// if (intersections.y > intersections.x) the ray hit the box, else it miss it
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// Assume dir is normalize
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float2 BoxRayIntersect(float3 start, float3 dir, float3 boxMin, float3 boxMax)
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{
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float3 invDir = 1.0 / dir;
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// Find the ray intersection with box plane
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float3 firstPlaneIntersect = (boxMin - start) * invDir;
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float3 secondPlaneIntersect = (boxMax - start) * invDir;
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// Get the closest/furthest of these intersections along the ray (Ok because x/0 give +inf and -x/0 give -inf )
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float3 closestPlane = min(firstPlaneIntersect, secondPlaneIntersect);
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float3 furthestPlane = max(firstPlaneIntersect, secondPlaneIntersect);
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float2 intersections;
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// Find the furthest near intersection
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intersections.x = max(closestPlane.x, max(closestPlane.y, closestPlane.z));
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// Find the closest far intersection
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intersections.y = min(min(furthestPlane.x, furthestPlane.y), furthestPlane.z);
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return intersections;
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}
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// This simplified version assume that we care about the result only when we are inside the box
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// Assume dir is normalize
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float BoxRayIntersectSimple(float3 start, float3 dir, float3 boxMin, float3 boxMax)
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{
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float3 invDir = 1.0 / dir;
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// Find the ray intersection with box plane
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float3 rbmin = (boxMin - start) * invDir;
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float3 rbmax = (boxMax - start) * invDir;
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float3 rbminmax = (dir > 0.0) ? rbmax : rbmin;
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return min(min(rbminmax.x, rbminmax.y), rbminmax.z);
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}
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// Assume Sphere is at the origin (i.e start = position - spherePosition)
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float2 SphereRayIntersect(float3 start, float3 dir, float radius, out bool intersect)
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{
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float a = dot(dir, dir);
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float b = dot(dir, start) * 2.0;
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float c = dot(start, start) - radius * radius;
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float discriminant = b * b - 4.0 * a * c;
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float2 intersections = float2(0.0, 0.0);
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intersect = false;
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if (discriminant < 0.0 || a == 0.0)
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{
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intersections.x = 0.0;
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intersections.y = 0.0;
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}
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else
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{
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float sqrtDiscriminant = sqrt(discriminant);
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intersections.x = (-b - sqrtDiscriminant) / (2.0 * a);
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intersections.y = (-b + sqrtDiscriminant) / (2.0 * a);
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intersect = true;
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}
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return intersections;
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}
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// This simplified version assume that we care about the result only when we are inside the sphere
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// Assume Sphere is at the origin (i.e start = position - spherePosition) and dir is normalized
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// Ref: http://http.developer.nvidia.com/GPUGems/gpugems_ch19.html
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float SphereRayIntersectSimple(float3 start, float3 dir, float radius)
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{
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float b = dot(dir, start) * 2.0;
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float c = dot(start, start) - radius * radius;
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float discriminant = b * b - 4.0 * c;
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return abs(sqrt(discriminant) - b) * 0.5;
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}
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float3 RayPlaneIntersect(in float3 rayOrigin, in float3 rayDirection, in float3 planeOrigin, in float3 planeNormal)
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{
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float dist = dot(planeNormal, planeOrigin - rayOrigin) / dot(planeNormal, rayDirection);
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return rayOrigin + rayDirection * dist;
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}
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//-----------------------------------------------------------------------------
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// Miscellaneous functions
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//-----------------------------------------------------------------------------
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// Box is AABB
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float DistancePointBox(float3 position, float3 boxMin, float3 boxMax)
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{
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return length(max(max(position - boxMax, boxMin - position), float3(0.0, 0.0, 0.0)));
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}
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float3 ProjectPointOnPlane(float3 position, float3 planePosition, float3 planeNormal)
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{
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return position - (dot(position - planePosition, planeNormal) * planeNormal);
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}
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// Plane equation: {(a, b, c) = N, d = -dot(N, P)}.
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// Returns the distance from the plane to the point 'p' along the normal.
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// Positive -> in front (above), negative -> behind (below).
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float DistanceFromPlane(float3 p, float4 plane)
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{
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return dot(float4(p, 1.0), plane);
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}
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// Returns 'true' if the triangle is outside of the frustum.
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// 'epsilon' is the (negative) distance to (outside of) the frustum below which we cull the triangle.
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bool CullTriangleFrustum(float3 p0, float3 p1, float3 p2, float epsilon, float4 frustumPlanes[6], int numPlanes)
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{
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bool outside = false;
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for (int i = 0; i < numPlanes; i++)
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{
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// If all 3 points are behind any of the planes, we cull.
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outside = outside || Max3(DistanceFromPlane(p0, frustumPlanes[i]),
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DistanceFromPlane(p1, frustumPlanes[i]),
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DistanceFromPlane(p2, frustumPlanes[i])) < epsilon;
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}
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return outside;
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}
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// Returns 'true' if the edge of the triangle is outside of the frustum.
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// The edges are defined s.t. they are on the opposite side of the point with the given index.
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// 'epsilon' is the (negative) distance to (outside of) the frustum below which we cull the triangle.
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bool3 CullTriangleEdgesFrustum(float3 p0, float3 p1, float3 p2, float epsilon, float4 frustumPlanes[6], int numPlanes)
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{
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bool3 edgesOutside = false;
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for (int i = 0; i < numPlanes; i++)
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{
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bool3 pointsOutside = bool3(DistanceFromPlane(p0, frustumPlanes[i]) < epsilon,
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DistanceFromPlane(p1, frustumPlanes[i]) < epsilon,
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DistanceFromPlane(p2, frustumPlanes[i]) < epsilon);
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// If both points of the edge are behind any of the planes, we cull.
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edgesOutside.x = edgesOutside.x || (pointsOutside.y && pointsOutside.z);
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edgesOutside.y = edgesOutside.y || (pointsOutside.x && pointsOutside.z);
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edgesOutside.z = edgesOutside.z || (pointsOutside.x && pointsOutside.y);
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}
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return edgesOutside;
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}
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// Returns 'true' if a triangle defined by 3 vertices is back-facing.
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// 'epsilon' is the (negative) value of dot(N, V) below which we cull the triangle.
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// 'winding' can be used to change the order: pass 1 for (p0 -> p1 -> p2), or -1 for (p0 -> p2 -> p1).
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bool CullTriangleBackFace(float3 p0, float3 p1, float3 p2, float epsilon, float3 viewPos, float winding)
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{
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float3 edge1 = p1 - p0;
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float3 edge2 = p2 - p0;
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float3 N = cross(edge1, edge2);
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float3 V = viewPos - p0;
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float NdotV = dot(N, V) * winding;
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// Optimize:
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// NdotV / (length(N) * length(V)) < Epsilon
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// NdotV < Epsilon * length(N) * length(V)
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// NdotV < Epsilon * sqrt(dot(N, N)) * sqrt(dot(V, V))
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// NdotV < Epsilon * sqrt(dot(N, N) * dot(V, V))
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return NdotV < epsilon * sqrt(dot(N, N) * dot(V, V));
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}
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#endif // UNITY_GEOMETRICTOOLS_INCLUDED
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