Developer CD Series 1995 August: Tool Chest/Dev.CD Aug 95 TC/Dev.CD Aug 95 TC.toast/New System Software Extensions/QuickDraw™ 3D 1.0/Development/Interfaces/QD3DMath.h

C/C++ Source or Header | 1995-06-02 | 24.0 KB | 880 lines | [TEXT/MPS ]

/******************************************************************************
 **                                                                             **
 **     Module:        QD3DMath.h                                                 **
 **                                                                          **
 **                                                                          **
 **     Purpose:     Math & matrix routines and definitions.                     **
 **                                                                          **
 **                                                                          **
 **                                                                          **
 **     Copyright (C) 1992-1995 Apple Computer, Inc.  All rights reserved.     **
 **                                                                          **
 **                                                                          **
 *****************************************************************************/
#ifndef QD3DMath_h
#define QD3DMath_h

#ifndef QD3D_h
#include "QD3D.h"
#endif  /*  QD3D_h  */

#if PRAGMA_ONCE
    #pragma once
#endif

#include <math.h>
#include <float.h>

#ifdef __cplusplus
extern "C" {
#endif    /* __cplusplus */

/******************************************************************************
 **                                                                             **
 **                            Constant Definitions                             **
 **                                                                             **
 *****************************************************************************/
/*
 *  Real zero definition
 */
#ifdef FLT_EPSILON
#    define kQ3RealZero            (FLT_EPSILON)
#else
#    define kQ3RealZero            ((float)1.19209290e-07)
#endif  /*  FLT_EPSILON  */

#ifdef FLT_MAX
#    define    kQ3MaxFloat            (FLT_MAX)
#else
#    define    kQ3MaxFloat            ((float)3.40282347e+38)
#endif  /*  FLT_MAX  */

/*
 *  Values of PI
 */
#define kQ3Pi                     ((float)3.1415926535898)
#define kQ32Pi                     ((float)(2.0 * 3.1415926535898))
#define kQ3PiOver2                ((float)(3.1415926535898 / 2.0))
#define kQ33PiOver2                ((float)(3.0 * 3.1415926535898 / 2.0))


/******************************************************************************
 **                                                                             **
 **                            Miscellaneous Functions                             **
 **                                                                             **
 *****************************************************************************/

#define Q3Math_DegreesToRadians(x)    ((float)((x) *  kQ3Pi / 180.0))
#define Q3Math_RadiansToDegrees(x)    ((float)((x) * 180.0 / kQ3Pi))

#define Q3Math_Min(x,y)                ((x) <= (y) ? (x) : (y))
#define Q3Math_Max(x,y)                ((x) >= (y) ? (x) : (y))


/******************************************************************************
 **                                                                             **
 **                            Point and Vector Creation                         **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Point2D *Q3Point2D_Set(
    TQ3Point2D                    *point2D,
    float                        x,
    float                        y);

QD3D_EXPORT TQ3Param2D *Q3Param2D_Set(
    TQ3Param2D                    *param2D,
    float                        u,
    float                        v);

QD3D_EXPORT TQ3Point3D *Q3Point3D_Set(
    TQ3Point3D                    *point3D,
    float                        x,
    float                        y,
    float                        z);

QD3D_EXPORT TQ3RationalPoint3D *Q3RationalPoint3D_Set(
    TQ3RationalPoint3D            *point3D,
    float                        x,
    float                        y,
    float                        w);

QD3D_EXPORT TQ3RationalPoint4D *Q3RationalPoint4D_Set(
    TQ3RationalPoint4D            *point4D,
    float                        x,
    float                        y,
    float                        z,
    float                        w);

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Set(
    TQ3Vector2D                    *vector2D,
    float                        x,
    float                        y);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Set(
    TQ3Vector3D                    *vector3D,
    float                        x,
    float                        y,
    float                        z);

QD3D_EXPORT TQ3PolarPoint *Q3PolarPoint_Set(
    TQ3PolarPoint                *polarPoint,
    float                        r,
    float                        theta);

QD3D_EXPORT TQ3SphericalPoint *Q3SphericalPoint_Set(
    TQ3SphericalPoint            *sphericalPoint,
    float                        rho,
    float                        theta,
    float                        phi);


/******************************************************************************
 **                                                                             **
 **                    Point and Vector Dimension Conversion                     **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Point3D *Q3Point2D_To3D(
    const TQ3Point2D            *point2D,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3Point2D *Q3RationalPoint3D_To2D(
    const TQ3RationalPoint3D    *point3D,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3RationalPoint4D *Q3Point3D_To4D(
    const TQ3Point3D            *point3D,
    TQ3RationalPoint4D            *result);

QD3D_EXPORT TQ3Point3D *Q3RationalPoint4D_To3D(
    const TQ3RationalPoint4D    *point4D,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector2D_To3D(
    const TQ3Vector2D            *vector2D,
    TQ3Vector3D                    *result);

QD3D_EXPORT TQ3Vector2D *Q3Vector3D_To2D(
    const TQ3Vector3D            *vector3D,
    TQ3Vector2D                    *result);


/******************************************************************************
 **                                                                             **
 **                            Point Subtraction                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Point2D_Subtract(
    const TQ3Point2D            *p1,
    const TQ3Point2D            *p2,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector2D *Q3Param2D_Subtract(
    const TQ3Param2D            *p1,
    const TQ3Param2D            *p2,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Point3D_Subtract(
    const TQ3Point3D            *p1,
    const TQ3Point3D            *p2,
    TQ3Vector3D                    *result);


/******************************************************************************
 **                                                                             **
 **                            Point Distance                                     **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT float Q3Point2D_Distance(
    const TQ3Point2D            *p1,
    const TQ3Point2D            *p2);

QD3D_EXPORT float Q3Point2D_DistanceSquared(
    const TQ3Point2D            *p1,
    const TQ3Point2D            *p2);


QD3D_EXPORT float Q3Param2D_Distance(
    const TQ3Param2D            *p1,
    const TQ3Param2D            *p2);

QD3D_EXPORT float Q3Param2D_DistanceSquared(
    const TQ3Param2D            *p1,
    const TQ3Param2D            *p2);


QD3D_EXPORT float Q3RationalPoint3D_Distance(
    const TQ3RationalPoint3D    *p1,
    const TQ3RationalPoint3D    *p2);

QD3D_EXPORT float Q3RationalPoint3D_DistanceSquared(
    const TQ3RationalPoint3D    *p1,
    const TQ3RationalPoint3D    *p2);


QD3D_EXPORT float Q3Point3D_Distance(
    const TQ3Point3D            *p1,
    const TQ3Point3D            *p2);

QD3D_EXPORT float Q3Point3D_DistanceSquared(
    const TQ3Point3D            *p1,
    const TQ3Point3D            *p2);


QD3D_EXPORT float Q3RationalPoint4D_Distance(
    const TQ3RationalPoint4D    *p1,
    const TQ3RationalPoint4D    *p2);

QD3D_EXPORT float Q3RationalPoint4D_DistanceSquared(
    const TQ3RationalPoint4D    *p1,
    const TQ3RationalPoint4D    *p2);


/******************************************************************************
 **                                                                             **
 **                            Point Relative Ratio                             **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Point2D *Q3Point2D_RRatio(
    const TQ3Point2D            *p1,
    const TQ3Point2D            *p2,
    float                        r1,
    float                        r2,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3Param2D *Q3Param2D_RRatio(
    const TQ3Param2D            *p1,
    const TQ3Param2D            *p2,
    float                        r1,
    float                        r2,
    TQ3Param2D                    *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_RRatio(
    const TQ3Point3D            *p1,
    const TQ3Point3D            *p2,
    float                        r1,
    float                        r2,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3RationalPoint4D *Q3RationalPoint4D_RRatio(
    const TQ3RationalPoint4D    *p1,
    const TQ3RationalPoint4D    *p2,
    float                        r1,
    float                        r2,
    TQ3RationalPoint4D            *result);


/******************************************************************************
 **                                                                             **
 **                    Point / Vector Addition    & Subtraction                     **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Point2D *Q3Point2D_Vector2D_Add(
    const TQ3Point2D            *point2D,
    const TQ3Vector2D            *vector2D,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3Param2D *Q3Param2D_Vector2D_Add(
    const TQ3Param2D            *param2D,
    const TQ3Vector2D            *vector2D,
    TQ3Param2D                    *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_Vector3D_Add(
    const TQ3Point3D            *point3D,
    const TQ3Vector3D            *vector3D,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3Point2D *Q3Point2D_Vector2D_Subtract(
    const TQ3Point2D            *point2D,
    const TQ3Vector2D            *vector2D,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3Param2D *Q3Param2D_Vector2D_Subtract(
    const TQ3Param2D            *param2D,
    const TQ3Vector2D            *vector2D,
    TQ3Param2D                    *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_Vector3D_Subtract(
    const TQ3Point3D            *point3D,
    const TQ3Vector3D            *vector3D,
    TQ3Point3D                    *result);


/******************************************************************************
 **                                                                             **
 **                                Vector Scale                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Scale(
    const TQ3Vector2D            *vector2D,
    float                        scalar,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Scale(
    const TQ3Vector3D            *vector3D,
    float                        scalar,
    TQ3Vector3D                    *result);


/******************************************************************************
 **                                                                             **
 **                                Vector Length                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT float Q3Vector2D_Length(
    const TQ3Vector2D             *vector2D);

QD3D_EXPORT float Q3Vector3D_Length(
    const TQ3Vector3D            *vector3D);


/******************************************************************************
 **                                                                             **
 **                                Vector Normalize                             **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Normalize(
    const TQ3Vector2D            *vector2D,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Normalize(
    const TQ3Vector3D            *vector3D,
    TQ3Vector3D                    *result);


/******************************************************************************
 **                                                                             **
 **                    Vector/Vector Addition and Subtraction                     **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Add(
    const TQ3Vector2D            *v1,
    const TQ3Vector2D            *v2,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Add(
    const TQ3Vector3D            *v1,
    const TQ3Vector3D            *v2,
    TQ3Vector3D                    *result);


QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Subtract(
    const TQ3Vector2D            *v1,
    const TQ3Vector2D            *v2,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Subtract(
    const TQ3Vector3D            *v1,
    const TQ3Vector3D            *v2,
    TQ3Vector3D                    *result);


/******************************************************************************
 **                                                                             **
 **                                Cross Product                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT float Q3Vector2D_Cross(
    const TQ3Vector2D            *v1,
    const TQ3Vector2D            *v2);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Cross(
    const TQ3Vector3D            *v1,
    const TQ3Vector3D            *v2,
    TQ3Vector3D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Point3D_CrossProductTri(
    const TQ3Point3D             *point1,
    const TQ3Point3D             *point2,
    const TQ3Point3D             *point3,
    TQ3Vector3D                 *crossVector);


/******************************************************************************
 **                                                                             **
 **                                Dot Product                                     **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT float Q3Vector2D_Dot(
    const TQ3Vector2D            *v1,
    const TQ3Vector2D            *v2);

QD3D_EXPORT float Q3Vector3D_Dot(
    const TQ3Vector3D            *v1,
    const TQ3Vector3D            *v2);


/******************************************************************************
 **                                                                             **
 **                        Point and Vector Transformation                         **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Transform(
    const TQ3Vector2D            *vector2D,
    const TQ3Matrix3x3             *matrix3x3,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Transform(
    const TQ3Vector3D            *vector3D,
    const TQ3Matrix4x4            *matrix4x4,
    TQ3Vector3D                    *result);

QD3D_EXPORT TQ3Point2D *Q3Point2D_Transform(
    const TQ3Point2D             *point2D,
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3Param2D *Q3Param2D_Transform(
    const TQ3Param2D             *param2D,
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Param2D                    *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_Transform(
    const TQ3Point3D            *point3D,
    const TQ3Matrix4x4            *matrix4x4,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3RationalPoint4D *Q3RationalPoint4D_Transform(
    const TQ3RationalPoint4D    *point4D,
    const TQ3Matrix4x4            *matrix4x4,
    TQ3RationalPoint4D            *result);

QD3D_EXPORT TQ3Status Q3Point3D_To3DTransformArray(
    const TQ3Point3D             *inVertex,
    const TQ3Matrix4x4             *matrix,
    TQ3Point3D                     *outVertex,
    long                         numVertices,
    unsigned long                 inStructSize,
    unsigned long                 outStructSize);

QD3D_EXPORT TQ3Status Q3Point3D_To4DTransformArray(
    const TQ3Point3D             *inVertex,
    const TQ3Matrix4x4             *matrix,
    TQ3RationalPoint4D             *outVertex,
    long                         numVertices,
    unsigned long                 inStructSize,
    unsigned long                 outStructSize);

QD3D_EXPORT TQ3Status Q3RationalPoint4D_To4DTransformArray(
    const TQ3RationalPoint4D     *inVertex,
    const TQ3Matrix4x4             *matrix,
    TQ3RationalPoint4D             *outVertex,
    long                         numVertices,
    unsigned long                 inStructSize,
    unsigned long                 outStructSize);


/******************************************************************************
 **                                                                             **
 **                                Vector Negation                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Vector2D *Q3Vector2D_Negate(
    const TQ3Vector2D            *vector2D,
    TQ3Vector2D                    *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_Negate(
    const TQ3Vector3D            *vector3D,
    TQ3Vector3D                    *result);


/******************************************************************************
 **                                                                             **
 **                    Point conversion from cartesian to polar                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3PolarPoint *Q3Point2D_ToPolar(
    const TQ3Point2D            *point2D,
    TQ3PolarPoint                *result);

QD3D_EXPORT TQ3Point2D *Q3PolarPoint_ToPoint2D(
    const TQ3PolarPoint            *polarPoint,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3SphericalPoint *Q3Point3D_ToSpherical(
    const TQ3Point3D            *point3D,
    TQ3SphericalPoint            *result);

QD3D_EXPORT TQ3Point3D *Q3SphericalPoint_ToPoint3D(
    const TQ3SphericalPoint        *sphericalPoint,
    TQ3Point3D                    *result);


/******************************************************************************
 **                                                                             **
 **                            Point Affine Combinations                         **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Point2D *Q3Point2D_AffineComb(
    const TQ3Point2D            *points2D,
    const float                    *weights,
    unsigned long                nPoints,
    TQ3Point2D                    *result);

QD3D_EXPORT TQ3Param2D *Q3Param2D_AffineComb(
    const TQ3Param2D            *param2Ds,
    const float                    *weights,
    unsigned long                nPoints,
    TQ3Param2D                    *result);

QD3D_EXPORT TQ3RationalPoint3D *Q3RationalPoint3D_AffineComb(
    const TQ3RationalPoint3D    *points3D,
    const float                    *weights,
    unsigned long                nPoints,
    TQ3RationalPoint3D            *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_AffineComb(
    const TQ3Point3D            *points3D,
    const float                    *weights,
    unsigned long                nPoints,
    TQ3Point3D                    *result);

QD3D_EXPORT TQ3RationalPoint4D *Q3RationalPoint4D_AffineComb(
    const TQ3RationalPoint4D    *points4D,
    const float                    *weights,
    unsigned long                nPoints,
    TQ3RationalPoint4D            *result);


/******************************************************************************
 **                                                                             **
 **                                Matrix Functions                             **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_Copy(
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Matrix3x3                *result);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_Copy(
    const TQ3Matrix4x4            *matrix4x4,
    TQ3Matrix4x4                *result);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_SetIdentity(
    TQ3Matrix3x3                *matrix3x3);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetIdentity(
    TQ3Matrix4x4                *matrix4x4);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_Transpose(
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Matrix3x3                *result);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_Transpose(
    const TQ3Matrix4x4            *matrix4x4,
    TQ3Matrix4x4                *result);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_Invert(
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Matrix3x3                *result);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_Invert(
    const TQ3Matrix4x4            *matrix4x4,
    TQ3Matrix4x4                *result);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_Adjoint(
    const TQ3Matrix3x3            *matrix3x3,
    TQ3Matrix3x3                *result);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_Multiply(
    const TQ3Matrix3x3            *matrixA,
    const TQ3Matrix3x3            *matrixB,
    TQ3Matrix3x3                *result);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_Multiply(
    const TQ3Matrix4x4            *matrixA,
    const TQ3Matrix4x4            *matrixB,
    TQ3Matrix4x4                *result);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_SetTranslate(
    TQ3Matrix3x3                *matrix3x3,
    float                        xTrans,
    float                        yTrans);

QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_SetScale(
    TQ3Matrix3x3                *matrix3x3,
    float                        xScale,
    float                        yScale);


QD3D_EXPORT TQ3Matrix3x3 *Q3Matrix3x3_SetRotateAboutPoint(
    TQ3Matrix3x3                *matrix3x3,
    const TQ3Point2D            *origin,
    float                        angle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetTranslate(
    TQ3Matrix4x4                *matrix4x4,
    float                        xTrans,
    float                        yTrans,
    float                        zTrans);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetScale(
    TQ3Matrix4x4                *matrix4x4,
    float                        xScale,
    float                        yScale,
    float                        zScale);


QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotateAboutPoint(
    TQ3Matrix4x4                *matrix4x4,
    const TQ3Point3D            *origin,
    float                        xAngle,
    float                        yAngle,
    float                        zAngle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotateAboutAxis(
    TQ3Matrix4x4                *matrix4x4,
    const TQ3Point3D            *origin,
    const TQ3Vector3D            *orientation,
    float                        angle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotate_X(
    TQ3Matrix4x4                *matrix4x4,
    float                        angle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotate_Y(
    TQ3Matrix4x4                *matrix4x4,
    float                        angle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotate_Z(
    TQ3Matrix4x4                *matrix4x4,
    float                        angle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotate_XYZ(
    TQ3Matrix4x4                *matrix4x4,
    float                        xAngle,
    float                        yAngle,
    float                        zAngle);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetRotateVectorToVector(
    TQ3Matrix4x4                *matrix4x4,
    const TQ3Vector3D            *v1,
    const TQ3Vector3D            *v2);

QD3D_EXPORT TQ3Matrix4x4 *Q3Matrix4x4_SetQuaternion(
    TQ3Matrix4x4                 *matrix,
    const TQ3Quaternion         *quaternion);

QD3D_EXPORT float Q3Matrix3x3_Determinant(
    const TQ3Matrix3x3            *matrix3x3);

QD3D_EXPORT float Q3Matrix4x4_Determinant(
    const TQ3Matrix4x4            *matrix4x4);


/******************************************************************************
 **                                                                             **
 **                                Quaternion Routines                             **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_Set(
    TQ3Quaternion                *quaternion,
    float                        w,
    float                        x,
    float                        y,
    float                        z);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetIdentity(
    TQ3Quaternion                *quaternion);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_Copy(
    const TQ3Quaternion            *quaternion,
    TQ3Quaternion                 *result);

QD3D_EXPORT TQ3Boolean Q3Quaternion_IsIdentity(
    const TQ3Quaternion            *quaternion);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_Invert(
    const TQ3Quaternion         *quaternion,
    TQ3Quaternion                *result);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_Normalize(
    const TQ3Quaternion            *quaternion,
    TQ3Quaternion                *result);

QD3D_EXPORT float Q3Quaternion_Dot(
    const TQ3Quaternion         *q1,
    const TQ3Quaternion         *q2);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_Multiply(
    const TQ3Quaternion            *q1,
    const TQ3Quaternion            *q2,
    TQ3Quaternion                *result);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateAboutAxis(
    TQ3Quaternion                 *quaternion,
    const TQ3Vector3D             *axis,
    float                         angle);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateXYZ(
    TQ3Quaternion                 *quaternion,
    float                         xAngle,
    float                         yAngle,
    float                         zAngle);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateX(
    TQ3Quaternion                 *quaternion,
    float                         angle);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateY(
    TQ3Quaternion                 *quaternion,
    float                         angle);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateZ(
    TQ3Quaternion                 *quaternion,
    float                         angle);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetMatrix(
    TQ3Quaternion                 *quaternion,
    const TQ3Matrix4x4             *matrix);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_SetRotateVectorToVector(
    TQ3Quaternion                 *quaternion,
    const TQ3Vector3D             *v1,
    const TQ3Vector3D             *v2);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_MatchReflection(
    const TQ3Quaternion            *q1,
    const TQ3Quaternion         *q2,
    TQ3Quaternion                *result);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_InterpolateFast(
    const TQ3Quaternion         *q1,
    const TQ3Quaternion         *q2,
    float                         t,
    TQ3Quaternion                *result);

QD3D_EXPORT TQ3Quaternion *Q3Quaternion_InterpolateLinear(
    const TQ3Quaternion         *q1,
    const TQ3Quaternion         *q2,
    float                         t,
    TQ3Quaternion                 *result);

QD3D_EXPORT TQ3Vector3D *Q3Vector3D_TransformQuaternion(
    const TQ3Vector3D             *vector,
    const TQ3Quaternion         *quaternion,
    TQ3Vector3D                    *result);

QD3D_EXPORT TQ3Point3D *Q3Point3D_TransformQuaternion(
    const TQ3Point3D             *vector,
    const TQ3Quaternion         *quaternion,
    TQ3Point3D                    *result);


/******************************************************************************
 **                                                                             **
 **                                Volume Routines                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_Copy(
    const TQ3BoundingBox         *src,
    TQ3BoundingBox                 *dest);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_Union(
    const TQ3BoundingBox         *v1,
    const TQ3BoundingBox         *v2,
    TQ3BoundingBox                *result);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_Set(
    TQ3BoundingBox                 *bBox,
    const TQ3Point3D             *min,
    const TQ3Point3D             *max,
    TQ3Boolean                    isEmpty);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_UnionPoint3D(
    const TQ3BoundingBox         *bBox,
    const TQ3Point3D             *pt3D,
    TQ3BoundingBox                *result);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_UnionRationalPoint4D(
    const TQ3BoundingBox         *bBox,
    const TQ3RationalPoint4D     *pt4D,
    TQ3BoundingBox                 *result);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_SetFromPoints3D(
    TQ3BoundingBox                 *bBox,
    const TQ3Point3D             *pts,
    unsigned long                 nPts,
    unsigned long                structSize);

QD3D_EXPORT TQ3BoundingBox *Q3BoundingBox_SetFromRationalPoints4D(
    TQ3BoundingBox                 *bBox,
    const TQ3RationalPoint4D     *pts,
    unsigned long                 nPts,
    unsigned long                structSize);


/******************************************************************************
 **                                                                             **
 **                                Sphere Routines                                 **
 **                                                                             **
 *****************************************************************************/

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_Copy(
    const TQ3BoundingSphere     *src,
    TQ3BoundingSphere             *dest);

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_Union(
    const TQ3BoundingSphere     *s1,
    const TQ3BoundingSphere     *s2,
    TQ3BoundingSphere            *result);

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_Set(
    TQ3BoundingSphere             *bSphere,
    const TQ3Point3D             *origin,
    float                        radius,
    TQ3Boolean                    isEmpty);

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_UnionPoint3D(
    const TQ3BoundingSphere     *bSphere,
    const TQ3Point3D             *pt3D,
    TQ3BoundingSphere            *result);

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_UnionRationalPoint4D(
    const TQ3BoundingSphere     *bSphere,
    const TQ3RationalPoint4D     *pt4D,
    TQ3BoundingSphere             *result);


QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_SetFromPoints3D(
    TQ3BoundingSphere             *bSphere,
    const TQ3Point3D             *pts,
    unsigned long                 nPts,
    unsigned long                structSize);

QD3D_EXPORT TQ3BoundingSphere *Q3BoundingSphere_SetFromRationalPoints4D(
    TQ3BoundingSphere             *bSphere,
    const TQ3RationalPoint4D     *pts,
    unsigned long                 nPts,
    unsigned long                structSize);


#ifdef __cplusplus
}
#endif    /* __cplusplus */

#endif  /*  QD3DMath_h  */