IceOBB.cpp

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// Precompiled Header
#include "Stdafx.h"

using namespace IceMaths;



bool OBB::ContainsPoint(const Point& p) const
{
        // Point in OBB test using lazy evaluation and early exits

        // Translate to box space
        Point RelPoint = p - mCenter;

        // Point * mRot maps from box space to world space
        // mRot * Point maps from world space to box space (what we need here)

        float f = mRot.m[0][0] * RelPoint.x + mRot.m[0][1] * RelPoint.y + mRot.m[0][2] * RelPoint.z;
        if(f >= mExtents.x || f <= -mExtents.x) return false;

        f = mRot.m[1][0] * RelPoint.x + mRot.m[1][1] * RelPoint.y + mRot.m[1][2] * RelPoint.z;
        if(f >= mExtents.y || f <= -mExtents.y) return false;

        f = mRot.m[2][0] * RelPoint.x + mRot.m[2][1] * RelPoint.y + mRot.m[2][2] * RelPoint.z;
        if(f >= mExtents.z || f <= -mExtents.z) return false;
        return true;
}



void OBB::Create(const AABB& aabb, const Matrix4x4& mat)
{
        // Note: must be coherent with Rotate()

        aabb.GetCenter(mCenter);
        aabb.GetExtents(mExtents);
        // Here we have the same as OBB::Rotate(mat) where the obb is (mCenter, mExtents, Identity).

        // So following what's done in Rotate:
        // - x-form the center
        mCenter *= mat;
        // - combine rotation with identity, i.e. just use given matrix
        mRot = mat;
}



bool OBB::ComputePlanes(Plane* planes)  const
{
        // Checkings
        if(!planes)     return false;

        Point Axis0 = mRot[0];
        Point Axis1 = mRot[1];
        Point Axis2 = mRot[2];

        // Writes normals
        planes[0].n = Axis0;
        planes[1].n = -Axis0;
        planes[2].n = Axis1;
        planes[3].n = -Axis1;
        planes[4].n = Axis2;
        planes[5].n = -Axis2;

        // Compute a point on each plane
        Point p0 = mCenter + Axis0 * mExtents.x;
        Point p1 = mCenter - Axis0 * mExtents.x;
        Point p2 = mCenter + Axis1 * mExtents.y;
        Point p3 = mCenter - Axis1 * mExtents.y;
        Point p4 = mCenter + Axis2 * mExtents.z;
        Point p5 = mCenter - Axis2 * mExtents.z;

        // Compute d
        planes[0].d = -(planes[0].n|p0);
        planes[1].d = -(planes[1].n|p1);
        planes[2].d = -(planes[2].n|p2);
        planes[3].d = -(planes[3].n|p3);
        planes[4].d = -(planes[4].n|p4);
        planes[5].d = -(planes[5].n|p5);

        return true;
}



bool OBB::ComputePoints(Point* pts)     const
{
        // Checkings
        if(!pts)        return false;

        Point Axis0 = mRot[0];
        Point Axis1 = mRot[1];
        Point Axis2 = mRot[2];

        Axis0 *= mExtents.x;
        Axis1 *= mExtents.y;
        Axis2 *= mExtents.z;

        //     7+------+6                       0 = ---
        //     /|     /|                        1 = +--
        //    / |    / |                        2 = ++-
        //   / 4+---/--+5                       3 = -+-
        // 3+------+2 /    y   z        4 = --+
        //  | /    | /     |  /         5 = +-+
        //  |/     |/      |/           6 = +++
        // 0+------+1      *---x        7 = -++

        pts[0] = mCenter - Axis0 - Axis1 - Axis2;
        pts[1] = mCenter + Axis0 - Axis1 - Axis2;
        pts[2] = mCenter + Axis0 + Axis1 - Axis2;
        pts[3] = mCenter - Axis0 + Axis1 - Axis2;
        pts[4] = mCenter - Axis0 - Axis1 + Axis2;
        pts[5] = mCenter + Axis0 - Axis1 + Axis2;
        pts[6] = mCenter + Axis0 + Axis1 + Axis2;
        pts[7] = mCenter - Axis0 + Axis1 + Axis2;

        return true;
}



bool OBB::ComputeVertexNormals(Point* pts)      const
{
        static float VertexNormals[] = 
        {
                -INVSQRT3,      -INVSQRT3,      -INVSQRT3,
                INVSQRT3,       -INVSQRT3,      -INVSQRT3,
                INVSQRT3,       INVSQRT3,       -INVSQRT3,
                -INVSQRT3,      INVSQRT3,       -INVSQRT3,
                -INVSQRT3,      -INVSQRT3,      INVSQRT3,
                INVSQRT3,       -INVSQRT3,      INVSQRT3,
                INVSQRT3,       INVSQRT3,       INVSQRT3,
                -INVSQRT3,      INVSQRT3,       INVSQRT3
        };

        if(!pts)        return false;

        const Point* VN = (const Point*)VertexNormals;
        for(udword i=0;i<8;i++)
        {
                pts[i] = VN[i] * mRot;
        }

        return true;
}



const udword* OBB::GetEdges() const
{
        static udword Indices[] = {
        0, 1,   1, 2,   2, 3,   3, 0,
        7, 6,   6, 5,   5, 4,   4, 7,
        1, 5,   6, 2,
        3, 7,   4, 0
        };
        return Indices;
}



const Point* OBB::GetLocalEdgeNormals() const
{
        static float EdgeNormals[] = 
        {
                0,                      -INVSQRT2,      -INVSQRT2,      // 0-1
                INVSQRT2,       0,                      -INVSQRT2,      // 1-2
                0,                      INVSQRT2,       -INVSQRT2,      // 2-3
                -INVSQRT2,      0,                      -INVSQRT2,      // 3-0

                0,                      INVSQRT2,       INVSQRT2,       // 7-6
                INVSQRT2,       0,                      INVSQRT2,       // 6-5
                0,                      -INVSQRT2,      INVSQRT2,       // 5-4
                -INVSQRT2,      0,                      INVSQRT2,       // 4-7

                INVSQRT2,       -INVSQRT2,      0,                      // 1-5
                INVSQRT2,       INVSQRT2,       0,                      // 6-2
                -INVSQRT2,      INVSQRT2,       0,                      // 3-7
                -INVSQRT2,      -INVSQRT2,      0                       // 4-0
        };
        return (const Point*)EdgeNormals;
}



void OBB::ComputeWorldEdgeNormal(udword edge_index, Point& world_normal) const
{
        ASSERT(edge_index<12);
        world_normal = GetLocalEdgeNormals()[edge_index] * mRot;
}



void OBB::ComputeLSS(LSS& lss) const
{
        Point Axis0 = mRot[0];
        Point Axis1 = mRot[1];
        Point Axis2 = mRot[2];

        switch(mExtents.LargestAxis())
        {
                case 0:
                        lss.mRadius = (mExtents.y + mExtents.z)*0.5f;
                        lss.mP0 = mCenter + Axis0 * (mExtents.x - lss.mRadius);
                        lss.mP1 = mCenter - Axis0 * (mExtents.x - lss.mRadius);
                        break;
                case 1:
                        lss.mRadius = (mExtents.x + mExtents.z)*0.5f;
                        lss.mP0 = mCenter + Axis1 * (mExtents.y - lss.mRadius);
                        lss.mP1 = mCenter - Axis1 * (mExtents.y - lss.mRadius);
                        break;
                case 2:
                        lss.mRadius = (mExtents.x + mExtents.y)*0.5f;
                        lss.mP0 = mCenter + Axis2 * (mExtents.z - lss.mRadius);
                        lss.mP1 = mCenter - Axis2 * (mExtents.z - lss.mRadius);
                        break;
        }
}



BOOL OBB::IsInside(const OBB& box) const
{
        // Make a 4x4 from the box & inverse it
        Matrix4x4 M0Inv;
        {
                Matrix4x4 M0 = box.mRot;
                M0.SetTrans(box.mCenter);
                InvertPRMatrix(M0Inv, M0);
        }

        // With our inversed 4x4, create box1 in space of box0
        OBB _1in0;
        Rotate(M0Inv, _1in0);

        // This should cancel out box0's rotation, i.e. it's now an AABB.
        // => Center(0,0,0), Rot(identity)

        // The two boxes are in the same space so now we can compare them.

        // Create the AABB of (box1 in space of box0)
        const Matrix3x3& mtx = _1in0.mRot;

        float f = fabsf(mtx.m[0][0] * mExtents.x) + fabsf(mtx.m[1][0] * mExtents.y) + fabsf(mtx.m[2][0] * mExtents.z) - box.mExtents.x;
        if(f > _1in0.mCenter.x)         return FALSE;
        if(-f < _1in0.mCenter.x)        return FALSE;

        f = fabsf(mtx.m[0][1] * mExtents.x) + fabsf(mtx.m[1][1] * mExtents.y) + fabsf(mtx.m[2][1] * mExtents.z) - box.mExtents.y;
        if(f > _1in0.mCenter.y)         return FALSE;
        if(-f < _1in0.mCenter.y)        return FALSE;

        f = fabsf(mtx.m[0][2] * mExtents.x) + fabsf(mtx.m[1][2] * mExtents.y) + fabsf(mtx.m[2][2] * mExtents.z) - box.mExtents.z;
        if(f > _1in0.mCenter.z)         return FALSE;
        if(-f < _1in0.mCenter.z)        return FALSE;

        return TRUE;
}