wmlintrbox3box3.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 "WmlIntrBox3Box3.h"
#include "WmlIntrUtilityLin3.h"
#include "WmlIntrUtilityBox3.h"
using namespace Wml;

//----------------------------------------------------------------------------
// stationary objects
//----------------------------------------------------------------------------
template <class Real>
bool Wml::TestIntersection (const Box3<Real>& rkBox0,
    const Box3<Real>& rkBox1)
{
    // Cutoff for cosine of angles between box axes.  This is used to catch
    // the cases when at least one pair of axes are parallel.  If this happens,
    // there is no need to test for separation along the Cross(A[i],B[j])
    // directions.
    const Real fCutoff = (Real)0.999999;
    bool bExistsParallelPair = false;
    int i;

    // convenience variables
    const Vector3<Real>* akA = rkBox0.Axes();
    const Vector3<Real>* akB = rkBox1.Axes();
    const Real* afEA = rkBox0.Extents();
    const Real* afEB = rkBox1.Extents();

    // compute difference of box centers, D = C1-C0
    Vector3<Real> kD = rkBox1.Center() - rkBox0.Center();

    Real aafC[3][3];     // matrix C = A^T B, c_{ij} = Dot(A_i,B_j)
    Real aafAbsC[3][3];  // |c_{ij}|
    Real afAD[3];        // Dot(A_i,D)
    Real fR0, fR1, fR;   // interval radii and distance between centers
    Real fR01;           // = R0 + R1

    // axis C0+t*A0
    for (i = 0; i < 3; i++)
    {
        aafC[0][i] = akA[0].Dot(akB[i]);
        aafAbsC[0][i] = Math<Real>::FAbs(aafC[0][i]);
        if ( aafAbsC[0][i] > fCutoff )
            bExistsParallelPair = true;
    }
    afAD[0] = akA[0].Dot(kD);
    fR = Math<Real>::FAbs(afAD[0]);
    fR1 = afEB[0]*aafAbsC[0][0]+afEB[1]*aafAbsC[0][1]+afEB[2]*aafAbsC[0][2];
    fR01 = afEA[0] + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A1
    for (i = 0; i < 3; i++)
    {
        aafC[1][i] = akA[1].Dot(akB[i]);
        aafAbsC[1][i] = Math<Real>::FAbs(aafC[1][i]);
        if ( aafAbsC[1][i] > fCutoff )
            bExistsParallelPair = true;
    }
    afAD[1] = akA[1].Dot(kD);
    fR = Math<Real>::FAbs(afAD[1]);
    fR1 = afEB[0]*aafAbsC[1][0]+afEB[1]*aafAbsC[1][1]+afEB[2]*aafAbsC[1][2];
    fR01 = afEA[1] + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A2
    for (i = 0; i < 3; i++)
    {
        aafC[2][i] = akA[2].Dot(akB[i]);
        aafAbsC[2][i] = Math<Real>::FAbs(aafC[2][i]);
        if ( aafAbsC[2][i] > fCutoff )
            bExistsParallelPair = true;
    }
    afAD[2] = akA[2].Dot(kD);
    fR = Math<Real>::FAbs(afAD[2]);
    fR1 = afEB[0]*aafAbsC[2][0]+afEB[1]*aafAbsC[2][1]+afEB[2]*aafAbsC[2][2];
    fR01 = afEA[2] + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*B0
    fR = Math<Real>::FAbs(akB[0].Dot(kD));
    fR0 = afEA[0]*aafAbsC[0][0]+afEA[1]*aafAbsC[1][0]+afEA[2]*aafAbsC[2][0];
    fR01 = fR0 + afEB[0];
    if ( fR > fR01 )
        return false;

    // axis C0+t*B1
    fR = Math<Real>::FAbs(akB[1].Dot(kD));
    fR0 = afEA[0]*aafAbsC[0][1]+afEA[1]*aafAbsC[1][1]+afEA[2]*aafAbsC[2][1];
    fR01 = fR0 + afEB[1];
    if ( fR > fR01 )
        return false;

    // axis C0+t*B2
    fR = Math<Real>::FAbs(akB[2].Dot(kD));
    fR0 = afEA[0]*aafAbsC[0][2]+afEA[1]*aafAbsC[1][2]+afEA[2]*aafAbsC[2][2];
    fR01 = fR0 + afEB[2];
    if ( fR > fR01 )
        return false;

    // At least one pair of box axes was parallel, so the separation is
    // effectively in 2D where checking the "edge" normals is sufficient for
    // the separation of the boxes.
    if ( bExistsParallelPair )
        return true;

    // axis C0+t*A0xB0
    fR = Math<Real>::FAbs(afAD[2]*aafC[1][0]-afAD[1]*aafC[2][0]);
    fR0 = afEA[1]*aafAbsC[2][0] + afEA[2]*aafAbsC[1][0];
    fR1 = afEB[1]*aafAbsC[0][2] + afEB[2]*aafAbsC[0][1];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A0xB1
    fR = Math<Real>::FAbs(afAD[2]*aafC[1][1]-afAD[1]*aafC[2][1]);
    fR0 = afEA[1]*aafAbsC[2][1] + afEA[2]*aafAbsC[1][1];
    fR1 = afEB[0]*aafAbsC[0][2] + afEB[2]*aafAbsC[0][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A0xB2
    fR = Math<Real>::FAbs(afAD[2]*aafC[1][2]-afAD[1]*aafC[2][2]);
    fR0 = afEA[1]*aafAbsC[2][2] + afEA[2]*aafAbsC[1][2];
    fR1 = afEB[0]*aafAbsC[0][1] + afEB[1]*aafAbsC[0][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A1xB0
    fR = Math<Real>::FAbs(afAD[0]*aafC[2][0]-afAD[2]*aafC[0][0]);
    fR0 = afEA[0]*aafAbsC[2][0] + afEA[2]*aafAbsC[0][0];
    fR1 = afEB[1]*aafAbsC[1][2] + afEB[2]*aafAbsC[1][1];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A1xB1
    fR = Math<Real>::FAbs(afAD[0]*aafC[2][1]-afAD[2]*aafC[0][1]);
    fR0 = afEA[0]*aafAbsC[2][1] + afEA[2]*aafAbsC[0][1];
    fR1 = afEB[0]*aafAbsC[1][2] + afEB[2]*aafAbsC[1][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A1xB2
    fR = Math<Real>::FAbs(afAD[0]*aafC[2][2]-afAD[2]*aafC[0][2]);
    fR0 = afEA[0]*aafAbsC[2][2] + afEA[2]*aafAbsC[0][2];
    fR1 = afEB[0]*aafAbsC[1][1] + afEB[1]*aafAbsC[1][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A2xB0
    fR = Math<Real>::FAbs(afAD[1]*aafC[0][0]-afAD[0]*aafC[1][0]);
    fR0 = afEA[0]*aafAbsC[1][0] + afEA[1]*aafAbsC[0][0];
    fR1 = afEB[1]*aafAbsC[2][2] + afEB[2]*aafAbsC[2][1];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A2xB1
    fR = Math<Real>::FAbs(afAD[1]*aafC[0][1]-afAD[0]*aafC[1][1]);
    fR0 = afEA[0]*aafAbsC[1][1] + afEA[1]*aafAbsC[0][1];
    fR1 = afEB[0]*aafAbsC[2][2] + afEB[2]*aafAbsC[2][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    // axis C0+t*A2xB2
    fR = Math<Real>::FAbs(afAD[1]*aafC[0][2]-afAD[0]*aafC[1][2]);
    fR0 = afEA[0]*aafAbsC[1][2] + afEA[1]*aafAbsC[0][2];
    fR1 = afEB[0]*aafAbsC[2][1] + afEB[1]*aafAbsC[2][0];
    fR01 = fR0 + fR1;
    if ( fR > fR01 )
        return false;

    return true;
}
//----------------------------------------------------------------------------
// moving objects
//----------------------------------------------------------------------------
template <class Real>
static bool BoxAxisFind (const Vector3<Real>& rkVelocity, 
    const Vector3<Real>& rkAxis, const Box3<Real>& rkBoxU,
    const Box3<Real>& rkBoxV, Real& rfTFirst, Real& rfTLast, Real fTMax,
    ContactSide& reSide, ContactConfig<Real>& rkTUC,
    ContactConfig<Real>& rkTVC)
{
    ContactConfig<Real> kUC;
    GetBoxConfiguration(rkAxis,rkBoxU,kUC);

    ContactConfig<Real> kVC;
    GetBoxConfiguration(rkAxis,rkBoxV,kVC);

    return AxisFind(rkVelocity,rkAxis,kUC,kVC,reSide,rkTUC,rkTVC,rfTFirst,
        rfTLast,fTMax);
}
//----------------------------------------------------------------------------
template <class Real>
static void FindContactSetCoplanarRectRect (const Vector3<Real> akFace0[4],
    const Vector3<Real> akFace1[4], int& riQuantity, Vector3<Real>* akP)
{
    // The potential intersection is initialized to face 0, and then clipped
    // against the four sides of face 1.

    riQuantity = 4;
    memcpy(akP,akFace0,4*sizeof(Vector3<Real>));

    for (int i0 = 3, i1 = 0; i1 < 4; i0 = i1++)
    {
        Vector3<Real> kNormal = akFace1[i1] - akFace1[i0];
        Real fConstant = kNormal.Dot(akFace1[i0]);
        ClipConvexPolygonAgainstPlane(kNormal,fConstant,riQuantity,akP);
    }
}
//----------------------------------------------------------------------------
template <class Real>
static void FindContactSet (const Box3<Real>& rkBox0,
    const Box3<Real>& rkBox1, ContactSide eSide,
    const ContactConfig<Real>& rkUC, const ContactConfig<Real>& rkVC, 
    const Vector3<Real>& rkVel0, const Vector3<Real>& rkVel1,
    Real fTFirst, int& riQuantity, Vector3<Real>* akP)
{
    // move boxes to new position
    Box3<Real> kNewBox0, kNewBox1;
    kNewBox0.Center() = rkBox0.Center() + fTFirst*rkVel0;
    kNewBox1.Center() = rkBox1.Center() + fTFirst*rkVel1;
    for (int i = 0; i < 3; i++)
    {
        kNewBox0.Axis(i) = rkBox0.Axis(i);
        kNewBox0.Extent(i) = rkBox0.Extent(i);
        kNewBox1.Axis(i) = rkBox1.Axis(i);
        kNewBox1.Extent(i) = rkBox1.Extent(i);
    }

    if ( eSide == LEFT )
    {
        // box1 on left of box0
        if ( rkUC.m_kMap == m1_1 )
        {
            riQuantity = 1;
            akP[0] = GetPoint(rkUC.m_aiIndex[0],kNewBox0);
        }
        else if ( rkVC.m_kMap == m1_1 )
        {
            riQuantity = 1;
            akP[0] = GetPoint(rkVC.m_aiIndex[7],kNewBox1);
        }
        else if ( rkUC.m_kMap == m2_2 )
        {
            if ( rkVC.m_kMap == m2_2 )
            {
                // box0edge-box1edge intersection
                Vector3<Real> akEdge0[2], akEdge1[2];
                akEdge0[0] = GetPoint(rkUC.m_aiIndex[0],kNewBox0);
                akEdge0[1] = GetPoint(rkUC.m_aiIndex[1],kNewBox0);
                akEdge1[0] = GetPoint(rkVC.m_aiIndex[6],kNewBox1);
                akEdge1[1] = GetPoint(rkVC.m_aiIndex[7],kNewBox1);
                FindContactSetLinLin(akEdge0,akEdge1,riQuantity,akP);
            }
            else // rkVC.m_kMap == m44
            {
                // box0edge-box1face intersection
                Vector3<Real> akEdge0[2], akFace1[4];
                akEdge0[0] = GetPoint(rkUC.m_aiIndex[0],kNewBox0);
                akEdge0[1] = GetPoint(rkUC.m_aiIndex[1],kNewBox0); 
                akFace1[0] = GetPoint(rkVC.m_aiIndex[4],kNewBox1); 
                akFace1[1] = GetPoint(rkVC.m_aiIndex[5],kNewBox1); 
                akFace1[2] = GetPoint(rkVC.m_aiIndex[6],kNewBox1); 
                akFace1[3] = GetPoint(rkVC.m_aiIndex[7],kNewBox1); 
                FindContactSetCoplanarLineRect(akEdge0,akFace1,riQuantity,
                    akP);
            }
        }
        else // rkUC.m_kMap == m44
        {
            if ( rkVC.m_kMap == m2_2 )
            {
                // box0face-box1edge intersection
                Vector3<Real> akFace0[4], akEdge1[2];
                akFace0[0] = GetPoint(rkUC.m_aiIndex[0],kNewBox0);
                akFace0[1] = GetPoint(rkUC.m_aiIndex[1],kNewBox0);
                akFace0[2] = GetPoint(rkUC.m_aiIndex[2],kNewBox0);
                akFace0[3] = GetPoint(rkUC.m_aiIndex[3],kNewBox0);
                akEdge1[0] = GetPoint(rkVC.m_aiIndex[6],kNewBox1);
                akEdge1[1] = GetPoint(rkVC.m_aiIndex[7],kNewBox1);
                FindContactSetCoplanarLineRect(akEdge1,akFace0,riQuantity,
                    akP);
            }
            else
            {
                // box0face-box1face intersection
                Vector3<Real> akFace0[4], akFace1[4];
                akFace0[0] = GetPoint(rkUC.m_aiIndex[0],kNewBox0);
                akFace0[1] = GetPoint(rkUC.m_aiIndex[1],kNewBox0);
                akFace0[2] = GetPoint(rkUC.m_aiIndex[2],kNewBox0);
                akFace0[3] = GetPoint(rkUC.m_aiIndex[3],kNewBox0);
                akFace1[0] = GetPoint(rkVC.m_aiIndex[4],kNewBox1);
                akFace1[1] = GetPoint(rkVC.m_aiIndex[5],kNewBox1);
                akFace1[2] = GetPoint(rkVC.m_aiIndex[6],kNewBox1);
                akFace1[3] = GetPoint(rkVC.m_aiIndex[7],kNewBox1);
                FindContactSetCoplanarRectRect(akFace0,akFace1,riQuantity,
                    akP);
            }
        }
    }
    else // rkSide == RIGHT 
    {
        // box1 on right of box0
        if ( rkUC.m_kMap == m1_1 )
        {
            riQuantity = 1;
            akP[0] = GetPoint(rkUC.m_aiIndex[7],kNewBox0);
        }
        else if ( rkVC.m_kMap == m1_1 )