411 lines
14 KiB
C
411 lines
14 KiB
C
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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2011, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHFRUSTUMTEST_H
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#define INCLUDED_IMATHFRUSTUMTEST_H
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//-------------------------------------------------------------------------
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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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//-------------------------------------------------------------------------
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#include "ImathFrustum.h"
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#include "ImathBox.h"
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#include "ImathSphere.h"
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#include "ImathMatrix.h"
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#include "ImathVec.h"
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namespace Imath {
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/////////////////////////////////////////////////////////////////
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// FrustumTest
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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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//////////////////////////////////////////////////////////////////
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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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//////////////////////////////////////////////////////////////////
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// Explanation of how it works
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//
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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>
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class FrustumTest
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{
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public:
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FrustumTest()
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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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FrustumTest(Frustum<T> &frustum, const Matrix44<T> &cameraMat)
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{
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setFrustum(frustum, cameraMat);
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}
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////////////////////////////////////////////////////////////////////
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// setFrustum()
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// This updates the frustum test with a new frustum and matrix.
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// This should usually be called just once per frame.
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void setFrustum(Frustum<T> &frustum, const Matrix44<T> &cameraMat);
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////////////////////////////////////////////////////////////////////
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// isVisible()
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// Check to see if shapes are visible.
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bool isVisible(const Sphere3<T> &sphere) const;
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bool isVisible(const Box<Vec3<T> > &box) const;
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bool isVisible(const Vec3<T> &vec) const;
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////////////////////////////////////////////////////////////////////
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// completelyContains()
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// Check to see if shapes are entirely contained.
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bool completelyContains(const Sphere3<T> &sphere) const;
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bool completelyContains(const Box<Vec3<T> > &box) const;
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// These next items are kept primarily for debugging tools.
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// It's useful for drawing the culling environment, and also
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// for getting an "outside view" of the culling frustum.
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Imath::Matrix44<T> cameraMat() const {return cameraMatrix;}
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Imath::Frustum<T> currentFrustum() const {return currFrustum;}
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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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Vec3<T> planeNormX[2]; // The X compunents from 6 plane equations
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Vec3<T> planeNormY[2]; // The Y compunents from 6 plane equations
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Vec3<T> planeNormZ[2]; // The Z compunents 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) compunents from 6 plane equations
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Vec3<T> planeNormAbsY[2]; // The abs(X) compunents from 6 plane equations
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Vec3<T> planeNormAbsZ[2]; // The abs(X) compunents 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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};
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////////////////////////////////////////////////////////////////////
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// setFrustum()
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// This should usually only be called once per frame, or however
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// often the camera moves.
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template<class T>
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void FrustumTest<T>::setFrustum(Frustum<T> &frustum,
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const Matrix44<T> &cameraMat)
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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>(Imath::abs(planeNormX[i].x),
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Imath::abs(planeNormX[i].y),
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Imath::abs(planeNormX[i].z));
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planeNormAbsY[i] = Vec3<T>(Imath::abs(planeNormY[i].x),
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Imath::abs(planeNormY[i].y),
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Imath::abs(planeNormY[i].z));
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planeNormAbsZ[i] = Vec3<T>(Imath::abs(planeNormZ[i].x),
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Imath::abs(planeNormZ[i].y),
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Imath::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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////////////////////////////////////////////////////////////////////
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// isVisible(Sphere)
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// Returns true if any part of the sphere is inside
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// the frustum.
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// The result MAY return close false-positives, but not false-negatives.
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//
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template<typename T>
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bool FrustumTest<T>::isVisible(const Sphere3<T> &sphere) const
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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
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+ planeNormY[0] * center.y
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+ planeNormZ[0] * center.z
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- radiusVec
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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] * center.x
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+ planeNormY[1] * center.y
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+ planeNormZ[1] * center.z
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- radiusVec
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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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////////////////////////////////////////////////////////////////////
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// completelyContains(Sphere)
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// Returns true if every part of the sphere is inside
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// the frustum.
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// The result MAY return close false-negatives, but not false-positives.
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//
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template<typename T>
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bool FrustumTest<T>::completelyContains(const Sphere3<T> &sphere) const
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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
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+ planeNormY[0] * center.y
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+ planeNormZ[0] * center.z
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+ radiusVec
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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] * center.x
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+ planeNormY[1] * center.y
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+ planeNormZ[1] * center.z
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+ radiusVec
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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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////////////////////////////////////////////////////////////////////
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// isVisible(Box)
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// Returns true if any part of the axis-aligned box
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// is inside the frustum.
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// The result MAY return close false-positives, but not false-negatives.
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//
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template<typename T>
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bool FrustumTest<T>::isVisible(const Box<Vec3<T> > &box) const
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{
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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
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+ planeNormY[0] * center.y
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+ planeNormZ[0] * center.z
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- planeNormAbsX[0] * extent.x
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- planeNormAbsY[0] * extent.y
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- planeNormAbsZ[0] * extent.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] * center.x
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+ planeNormY[1] * center.y
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+ planeNormZ[1] * center.z
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- planeNormAbsX[1] * extent.x
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- planeNormAbsY[1] * extent.y
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- planeNormAbsZ[1] * extent.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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////////////////////////////////////////////////////////////////////
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// completelyContains(Box)
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// Returns true if every part of the axis-aligned box
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// is inside the frustum.
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// The result MAY return close false-negatives, but not false-positives.
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//
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template<typename T>
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bool FrustumTest<T>::completelyContains(const Box<Vec3<T> > &box) const
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{
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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
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+ planeNormY[0] * center.y
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+ planeNormZ[0] * center.z
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+ planeNormAbsX[0] * extent.x
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+ planeNormAbsY[0] * extent.y
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+ planeNormAbsZ[0] * extent.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;
|
||
|
|
|
||
|
|
Vec3<T> 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////
|
||
|
|
// isVisible(Vec3)
|
||
|
|
// Returns true if the point is inside the frustum.
|
||
|
|
//
|
||
|
|
template<typename T>
|
||
|
|
bool FrustumTest<T>::isVisible(const Vec3<T> &vec) const
|
||
|
|
{
|
||
|
|
// This is a vertical dot-product on three vectors at once.
|
||
|
|
Vec3<T> 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<T> 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
typedef FrustumTest<float> FrustumTestf;
|
||
|
|
typedef FrustumTest<double> FrustumTestd;
|
||
|
|
|
||
|
|
} //namespace Imath
|
||
|
|
|
||
|
|
#endif
|