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// // SPDX-License-Identifier: BSD-3-Clause // Copyright Contributors to the OpenEXR Project. // // // A viewing frustum class // // This file contains algorithms applied to or in conjunction with // Frustum visibility testing (Imath::Frustum). // // Methods for frustum-based rejection of primitives are contained here. // #ifndef INCLUDED_IMATHFRUSTUMTEST_H #define INCLUDED_IMATHFRUSTUMTEST_H #include "ImathExport.h" #include "ImathNamespace.h" #include "ImathBox.h" #include "ImathFrustum.h" #include "ImathMatrix.h" #include "ImathSphere.h" #include "ImathVec.h" IMATH_INTERNAL_NAMESPACE_HEADER_ENTER /// /// template class FrustumTest /// /// This is a helper class, designed to accelerate the case /// where many tests are made against the same frustum. /// That's a really common case. /// /// The acceleration is achieved by pre-computing the planes of /// the frustum, along with the ablsolute values of the plane normals. /// /// How to use this /// /// Given that you already have: /// Imath::Frustum myFrustum /// Imath::Matrix44 myCameraWorldMatrix /// /// First, make a frustum test object: /// FrustumTest myFrustumTest(myFrustum, myCameraWorldMatrix) /// /// Whenever the camera or frustum changes, call: /// myFrustumTest.setFrustum(myFrustum, myCameraWorldMatrix) /// /// For each object you want to test for visibility, call: /// myFrustumTest.isVisible(myBox) /// myFrustumTest.isVisible(mySphere) /// myFrustumTest.isVisible(myVec3) /// myFrustumTest.completelyContains(myBox) /// myFrustumTest.completelyContains(mySphere) /// /// Explanation of how it works /// /// We store six world-space Frustum planes (nx, ny, nz, offset) /// /// Points: To test a Vec3 for visibility, test it against each plane /// using the normal (v dot n - offset) method. (the result is exact) /// /// BBoxes: To test an axis-aligned bbox, test the center against each plane /// using the normal (v dot n - offset) method, but offset by the /// box extents dot the abs of the plane normal. (the result is NOT /// exact, but will not return false-negatives.) /// /// Spheres: To test a sphere, test the center against each plane /// using the normal (v dot n - offset) method, but offset by the /// sphere's radius. (the result is NOT exact, but will not return /// false-negatives.) /// /// /// SPECIAL NOTE: "Where are the dot products?" /// Actual dot products are currently slow for most SIMD architectures. /// In order to keep this code optimization-ready, the dot products /// are all performed using vector adds and multipies. /// /// In order to do this, the plane equations are stored in "transpose" /// form, with the X components grouped into an X vector, etc. /// template class IMATH_EXPORT_TEMPLATE_TYPE FrustumTest { public: /// @{ /// @name Constructors /// Initialize camera matrix to identity FrustumTest () IMATH_NOEXCEPT { Frustum frust; Matrix44 cameraMat; cameraMat.makeIdentity (); setFrustum (frust, cameraMat); } /// Initialize to a given frustum and camera matrix. FrustumTest (const Frustum& frustum, const Matrix44& cameraMat) IMATH_NOEXCEPT { setFrustum (frustum, cameraMat); } /// @} /// @{ /// @name Set Value /// Update the frustum test with a new frustum and matrix. /// This should usually be called just once per frame, or however /// often the camera moves. void setFrustum (const Frustum& frustum, const Matrix44& cameraMat) IMATH_NOEXCEPT; /// @} /// @{ /// @name Query /// Return true if any part of the sphere is inside the frustum. /// The result MAY return close false-positives, but not false-negatives. bool isVisible (const Sphere3& sphere) const IMATH_NOEXCEPT; /// Return true if any part of the box is inside the frustum. /// The result MAY return close false-positives, but not false-negatives. bool isVisible (const Box>& box) const IMATH_NOEXCEPT; /// Return true if the point is inside the frustum. bool isVisible (const Vec3& vec) const IMATH_NOEXCEPT; /// Return true if every part of the sphere is inside the frustum. /// The result MAY return close false-negatives, but not false-positives. bool completelyContains (const Sphere3& sphere) const IMATH_NOEXCEPT; /// Return true if every part of the box is inside the frustum. /// The result MAY return close false-negatives, but not false-positives. bool completelyContains (const Box>& box) const IMATH_NOEXCEPT; /// Return the camera matrix (primarily for debugging) IMATH_INTERNAL_NAMESPACE::Matrix44 cameraMat () const IMATH_NOEXCEPT { return cameraMatrix; } /// Return the viewing frustum (primarily for debugging) IMATH_INTERNAL_NAMESPACE::Frustum currentFrustum () const IMATH_NOEXCEPT { return currFrustum; } /// @} typedef T BaseType; typedef T value_type; protected: // To understand why the planes are stored this way, see // the SPECIAL NOTE above. /// @cond Doxygen_Suppress Vec3 planeNormX[2]; // The X components from 6 plane equations Vec3 planeNormY[2]; // The Y components from 6 plane equations Vec3 planeNormZ[2]; // The Z components from 6 plane equations Vec3 planeOffsetVec[2]; // The distance offsets from 6 plane equations // The absolute values are stored to assist with bounding box tests. Vec3 planeNormAbsX[2]; // The abs(X) components from 6 plane equations Vec3 planeNormAbsY[2]; // The abs(X) components from 6 plane equations Vec3 planeNormAbsZ[2]; // The abs(X) components from 6 plane equations // These are kept primarily for debugging tools. Frustum currFrustum; Matrix44 cameraMatrix; /// @endcond }; template void FrustumTest::setFrustum ( const Frustum& frustum, const Matrix44& cameraMat) IMATH_NOEXCEPT { Plane3 frustumPlanes[6]; frustum.planes (frustumPlanes, cameraMat); // Here's where we effectively transpose the plane equations. // We stuff all six X's into the two planeNormX vectors, etc. for (int i = 0; i < 2; ++i) { int index = i * 3; planeNormX[i] = Vec3 ( frustumPlanes[index + 0].normal.x, frustumPlanes[index + 1].normal.x, frustumPlanes[index + 2].normal.x); planeNormY[i] = Vec3 ( frustumPlanes[index + 0].normal.y, frustumPlanes[index + 1].normal.y, frustumPlanes[index + 2].normal.y); planeNormZ[i] = Vec3 ( frustumPlanes[index + 0].normal.z, frustumPlanes[index + 1].normal.z, frustumPlanes[index + 2].normal.z); planeNormAbsX[i] = Vec3 ( std::abs (planeNormX[i].x), std::abs (planeNormX[i].y), std::abs (planeNormX[i].z)); planeNormAbsY[i] = Vec3 ( std::abs (planeNormY[i].x), std::abs (planeNormY[i].y), std::abs (planeNormY[i].z)); planeNormAbsZ[i] = Vec3 ( std::abs (planeNormZ[i].x), std::abs (planeNormZ[i].y), std::abs (planeNormZ[i].z)); planeOffsetVec[i] = Vec3 ( frustumPlanes[index + 0].distance, frustumPlanes[index + 1].distance, frustumPlanes[index + 2].distance); } currFrustum = frustum; cameraMatrix = cameraMat; } template bool FrustumTest::isVisible (const Sphere3& sphere) const IMATH_NOEXCEPT { Vec3 center = sphere.center; Vec3 radiusVec = Vec3 (sphere.radius, sphere.radius, sphere.radius); // This is a vertical dot-product on three vectors at once. Vec3 d0 = planeNormX[0] * center.x + planeNormY[0] * center.y + planeNormZ[0] * center.z - radiusVec - planeOffsetVec[0]; if (d0.x >= 0 || d0.y >= 0 || d0.z >= 0) return false; Vec3 d1 = planeNormX[1] * center.x + planeNormY[1] * center.y + planeNormZ[1] * center.z - radiusVec - planeOffsetVec[1]; if (d1.x >= 0 || d1.y >= 0 || d1.z >= 0) return false; return true; } template bool FrustumTest::completelyContains (const Sphere3& sphere) const IMATH_NOEXCEPT { Vec3 center = sphere.center; Vec3 radiusVec = Vec3 (sphere.radius, sphere.radius, sphere.radius); // This is a vertical dot-product on three vectors at once. Vec3 d0 = planeNormX[0] * center.x + planeNormY[0] * center.y + planeNormZ[0] * center.z + radiusVec - planeOffsetVec[0]; if (d0.x >= 0 || d0.y >= 0 || d0.z >= 0) return false; Vec3 d1 = planeNormX[1] * center.x + planeNormY[1] * center.y + planeNormZ[1] * center.z + radiusVec - planeOffsetVec[1]; if (d1.x >= 0 || d1.y >= 0 || d1.z >= 0) return false; return true; } template bool FrustumTest::isVisible (const Box>& box) const IMATH_NOEXCEPT { if (box.isEmpty ()) return false; Vec3 center = (box.min + box.max) / 2; Vec3 extent = (box.max - center); // This is a vertical dot-product on three vectors at once. Vec3 d0 = planeNormX[0] * center.x + planeNormY[0] * center.y + planeNormZ[0] * center.z - planeNormAbsX[0] * extent.x - planeNormAbsY[0] * extent.y - planeNormAbsZ[0] * extent.z - planeOffsetVec[0]; if (d0.x >= 0 || d0.y >= 0 || d0.z >= 0) return false; Vec3 d1 = planeNormX[1] * center.x + planeNormY[1] * center.y + planeNormZ[1] * center.z - planeNormAbsX[1] * extent.x - planeNormAbsY[1] * extent.y - planeNormAbsZ[1] * extent.z - planeOffsetVec[1]; if (d1.x >= 0 || d1.y >= 0 || d1.z >= 0) return false; return true; } template bool FrustumTest::completelyContains (const Box>& box) const IMATH_NOEXCEPT { if (box.isEmpty ()) return false; Vec3 center = (box.min + box.max) / 2; Vec3 extent = (box.max - center); // This is a vertical dot-product on three vectors at once. Vec3 d0 = planeNormX[0] * center.x + planeNormY[0] * center.y + planeNormZ[0] * center.z + planeNormAbsX[0] * extent.x + planeNormAbsY[0] * extent.y + planeNormAbsZ[0] * extent.z - planeOffsetVec[0]; if (d0.x >= 0 || d0.y >= 0 || d0.z >= 0) return false; Vec3 d1 = planeNormX[1] * center.x + planeNormY[1] * center.y + planeNormZ[1] * center.z + planeNormAbsX[1] * extent.x + planeNormAbsY[1] * extent.y + planeNormAbsZ[1] * extent.z - planeOffsetVec[1]; if (d1.x >= 0 || d1.y >= 0 || d1.z >= 0) return false; return true; } template bool FrustumTest::isVisible (const Vec3& vec) const IMATH_NOEXCEPT { // This is a vertical dot-product on three vectors at once. Vec3 d0 = (planeNormX[0] * vec.x) + (planeNormY[0] * vec.y) + (planeNormZ[0] * vec.z) - planeOffsetVec[0]; if (d0.x >= 0 || d0.y >= 0 || d0.z >= 0) return false; Vec3 d1 = (planeNormX[1] * vec.x) + (planeNormY[1] * vec.y) + (planeNormZ[1] * vec.z) - planeOffsetVec[1]; if (d1.x >= 0 || d1.y >= 0 || d1.z >= 0) return false; return true; } /// FrustymTest of type float typedef FrustumTest FrustumTestf; /// FrustymTest of type double typedef FrustumTest FrustumTestd; IMATH_INTERNAL_NAMESPACE_HEADER_EXIT #endif // INCLUDED_IMATHFRUSTUMTEST_H