quaternion.cpp

/*
    pbrt source code Copyright(c) 1998-2012 Matt Pharr and Greg Humphreys.

    This file is part of pbrt.

    Redistribution and use in source and binary forms, with or without
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    met:

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      notice, this list of conditions and the following disclaimer.

    - Redistributions in binary form must reproduce the above copyright
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      documentation and/or other materials provided with the distribution.

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
    IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
    TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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 */


// core/quaternion.cpp*
#include "stdafx.h"
#include "quaternion.h"
#include "transform.h"

// Quaternion Method Definitions
Transform Quaternion::ToTransform() const {
    float xx = v.x * v.x, yy = v.y * v.y, zz = v.z * v.z;
    float xy = v.x * v.y, xz = v.x * v.z, yz = v.y * v.z;
    float wx = v.x * w,   wy = v.y * w,   wz = v.z * w;

    Matrix4x4 m;
    m.m[0][0] = 1.f - 2.f * (yy + zz);
    m.m[0][1] =       2.f * (xy + wz);
    m.m[0][2] =       2.f * (xz - wy);
    m.m[1][0] =       2.f * (xy - wz);
    m.m[1][1] = 1.f - 2.f * (xx + zz);
    m.m[1][2] =       2.f * (yz + wx);
    m.m[2][0] =       2.f * (xz + wy);
    m.m[2][1] =       2.f * (yz - wx);
    m.m[2][2] = 1.f - 2.f * (xx + yy);

    // Transpose since we are left-handed.  Ugh.
    return Transform(Transpose(m), m);
}


Quaternion::Quaternion(const Transform &t) {
    const Matrix4x4 &m = t.m;
    float trace = m.m[0][0] + m.m[1][1] + m.m[2][2];
    if (trace > 0.f) {
        // Compute w from matrix trace, then xyz
        // 4w^2 = m[0][0] + m[1][1] + m[2][2] + m[3][3] (but m[3][3] == 1)
        float s = sqrtf(trace + 1.0);
        w = s / 2.0f;
        s = 0.5f / s;
        v.x = (m.m[2][1] - m.m[1][2]) * s;
        v.y = (m.m[0][2] - m.m[2][0]) * s;
        v.z = (m.m[1][0] - m.m[0][1]) * s;
    }
    else {
        // Compute largest of $x$, $y$, or $z$, then remaining components
        const int nxt[3] = {1, 2, 0};
        float q[3];
        int i = 0;
        if (m.m[1][1] > m.m[0][0]) i = 1;
        if (m.m[2][2] > m.m[i][i]) i = 2;
        int j = nxt[i];
        int k = nxt[j];
        float s = sqrtf((m.m[i][i] - (m.m[j][j] + m.m[k][k])) + 1.0);
        q[i] = s * 0.5f;
        if (s != 0.f) s = 0.5f / s;
        w = (m.m[k][j] - m.m[j][k]) * s;
        q[j] = (m.m[j][i] + m.m[i][j]) * s;
        q[k] = (m.m[k][i] + m.m[i][k]) * s;
        v.x = q[0];
        v.y = q[1];
        v.z = q[2];
    }
}


Quaternion Slerp(float t, const Quaternion &q1,
                 const Quaternion &q2) {
    float cosTheta = Dot(q1, q2);
    if (cosTheta > .9995f)
        return Normalize((1.f - t) * q1 + t * q2);
    else {
        float theta = acosf(Clamp(cosTheta, -1.f, 1.f));
        float thetap = theta * t;
        Quaternion qperp = Normalize(q2 - q1 * cosTheta);
        return q1 * cosf(thetap) + qperp * sinf(thetap);
    }
}