wmlrandomhypersphere.cpp

3D Game Engine Design Source Code非常棒

// Magic Software, Inc.
// http://www.magic-software.com
// http://www.wild-magic.com
// Copyright (c) 2003.  All Rights Reserved
//
// The Wild Magic Library (WML) source code is supplied under the terms of
// the license agreement http://www.magic-software.com/License/WildMagic.pdf
// and may not be copied or disclosed except in accordance with the terms of
// that agreement.

#include "WmlRandomHypersphere.h"
#include "WmlMath.h"
using namespace Wml;

//----------------------------------------------------------------------------
static void RecurseRandomPoint (int iDimension, double* adPoint)
{
    // select random point on circle
    double dAngle = Mathd::IntervalRandom(0.0,Mathd::TWO_PI);
    double dCos = Mathd::Cos(dAngle);
    double dSin = Mathd::Sin(dAngle);

    if ( iDimension > 3 )
    {
        // split components into two sets and adjust values
        int i, iHalf = iDimension/2;
        for (i = 0; i < iHalf; i++)
            adPoint[i] *= dCos;
        for (i = iHalf; i < iDimension; i++)
            adPoint[i] *= dSin;

        // recurse on each half of the components
        RecurseRandomPoint(iHalf,adPoint);
        RecurseRandomPoint(iDimension-iHalf,adPoint+iHalf);
    }
    else if ( iDimension == 3 )
    {
        double dValue = Mathd::SymmetricRandom();
        double dComplement = Mathd::Sqrt(Mathd::FAbs(1.0-dValue*dValue));
        adPoint[0] *= dValue;
        adPoint[1] *= dComplement*dCos;
        adPoint[2] *= dComplement*dSin;
    }
    else if ( iDimension == 2 )
    {
        adPoint[0] *= dCos;
        adPoint[1] *= dSin;
    }
}
//----------------------------------------------------------------------------
void Wml::RandomPointOnHypersphere (int iDimension, double* adPoint)
{
    for (int i = 0; i < iDimension; i++)
        adPoint[i] = 1.0;

    RecurseRandomPoint(iDimension,adPoint);
}
//----------------------------------------------------------------------------
void Wml::Histogram (int iDimension, double dAngle, int iQuantity,
    double** aadPoint, int* aiHistogram)
{
    // Count the number of points located in the cone of specified angle
    // about each of the samples.
    double dCos = Mathd::Cos(dAngle);

    for (int i = 0; i < iQuantity; i++)
    {
        aiHistogram[i] = 0;
        for (int j = 0; j < iQuantity; j++)
        {
            // compute dot product between points P[i] and P[j]
            double dDot = 0;
            for (int k = 0; k < iDimension; k++)
                dDot += aadPoint[i][k]*aadPoint[j][k];
            if ( dDot >= dCos )
                aiHistogram[i]++;
        }
    }
}
//----------------------------------------------------------------------------