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