Contents

• About the Mathematical Utilities
• QuickDraw 3D Mathematical Utilities Reference
• Data Structures
• Bounding Boxes
• Bounding Spheres
• QuickDraw 3D Mathematical Utilities
• Setting Points and Vectors
• Q3Point2D_Set
• Q3Param2D_Set
• Q3Point3D_Set
• Q3RationalPoint3D_Set
• Q3RationalPoint4D_Set
• Q3PolarPoint_Set
• Q3SphericalPoint_Set
• Q3Vector2D_Set
• Q3Vector3D_Set
• Converting Dimensions of Points and Vectors
• Q3Point2D_To3D
• Q3Point3D_To4D
• Q3RationalPoint3D_To2D
• Q3RationalPoint4D_To3D
• Q3Vector2D_To3D
• Q3Vector3D_To2D
• Subtracting Points
• Q3Point2D_Subtract
• Q3Param2D_Subtract
• Q3Point3D_Subtract
• Calculating Distances Between Points
• Q3Point2D_Distance
• Q3Param2D_Distance
• Q3Point3D_Distance
• Q3RationalPoint3D_Distance
• Q3RationalPoint4D_Distance
• Q3Point2D_DistanceSquared
• Q3Param2D_DistanceSquared
• Q3Point3D_DistanceSquared
• Q3RationalPoint3D_DistanceSquared
• Q3RationalPoint4D_DistanceSquared
• Determining Point Relative Ratios
• Q3Point2D_RRatio
• Q3Param2D_RRatio
• Q3Point3D_RRatio
• Q3RationalPoint4D_RRatio
• Adding and Subtracting Points and Vectors
• Q3Point2D_Vector2D_Add
• Q3Param2D_Vector2D_Add
• Q3Point3D_Vector3D_Add
• Q3Point2D_Vector2D_Subtract
• Q3Param2D_Vector2D_Subtract
• Q3Point3D_Vector3D_Subtract
• Scaling Vectors
• Q3Vector2D_Scale
• Q3Vector3D_Scale
• Determining the Lengths of Vectors
• Q3Vector2D_Length
• Q3Vector3D_Length
• Normalizing Vectors
• Q3Vector2D_Normalize
• Q3Vector3D_Normalize
• Adding and Subtracting Vectors
• Q3Vector2D_Add
• Q3Vector3D_Add
• Q3Vector2D_Subtract
• Q3Vector3D_Subtract
• Determining Vector Cross Products
• Q3Vector2D_Cross
• Q3Vector3D_Cross
• Q3Point3D_CrossProductTri
• Determining Vector Dot Products
• Q3Vector2D_Dot
• Q3Vector3D_Dot
• Transforming Points and Vectors
• Q3Vector2D_Transform
• Q3Vector3D_Transform
• Q3Point2D_Transform
• Q3Param2D_Transform
• Q3Point3D_Transform
• Q3RationalPoint4D_Transform
• Q3Point3D_To3DTransformArray
• Q3Point3D_To4DTransformArray
• Q3RationalPoint4D_To4DTransformArray
• Negating Vectors
• Q3Vector2D_Negate
• Q3Vector3D_Negate
• Converting Points from Cartesian to Polar or Spherical Form
• Q3Point2D_ToPolar
• Q3PolarPoint_ToPoint2D
• Q3Point3D_ToSpherical
• Q3SphericalPoint_ToPoint3D
• Determining Point Affine Combinations
• Q3Point2D_AffineComb
• Q3Param2D_AffineComb
• Q3Point3D_AffineComb
• Q3RationalPoint3D_AffineComb
• Q3RationalPoint4D_AffineComb
• Managing Matrices
• Q3Matrix3x3_Copy
• Q3Matrix4x4_Copy
• Q3Matrix3x3_SetIdentity
• Q3Matrix4x4_SetIdentity
• Q3Matrix3x3_Transpose
• Q3Matrix4x4_Transpose
• Q3Matrix3x3_Invert
• Q3Matrix4x4_Invert
• Q3Matrix3x3_Adjoint
• Q3Matrix3x3_Multiply
• Q3Matrix4x4_Multiply
• Q3Matrix3x3_Determinant
• Q3Matrix4x4_Determinant
• Setting Up Transformation Matrices
• Q3Matrix3x3_SetTranslate
• Q3Matrix3x3_SetScale
• Q3Matrix3x3_SetRotateAboutPoint
• Q3Matrix4x4_SetTranslate
• Q3Matrix4x4_SetScale
• Q3Matrix4x4_SetRotateAboutPoint
• Q3Matrix4x4_SetRotateAboutAxis
• Q3Matrix4x4_SetRotate_X
• Q3Matrix4x4_SetRotate_Y
• Q3Matrix4x4_SetRotate_Z
• Q3Matrix4x4_SetRotate_XYZ
• Q3Matrix4x4_SetRotateVectorToVector
• Q3Matrix4x4_SetQuaternion
• Utility Functions
• Managing Quaternions
• Q3Quaternion_Set
• Q3Quaternion_SetIdentity
• Q3Quaternion_Copy
• Q3Quaternion_IsIdentity
• Q3Quaternion_Invert
• Q3Quaternion_Normalize
• Q3Quaternion_Dot
• Q3Quaternion_Multiply
• Q3Quaternion_SetRotateAboutAxis
• Q3Quaternion_SetRotate_X
• Q3Quaternion_SetRotate_Y
• Q3Quaternion_SetRotate_Z
• Q3Quaternion_SetRotate_XYZ
• Q3Quaternion_SetMatrix
• Q3Quaternion_SetRotateVectorToVector
• Q3Quaternion_MatchReflection
• Q3Quaternion_InterpolateFast
• Q3Quaternion_InterpolateLinear
• Q3Vector3D_TransformQuaternion
• Q3Point3D_TransformQuaternion
• Managing Bounding Boxes
• Q3BoundingBox_Copy
• Q3BoundingBox_Union
• Q3BoundingBox_Set
• Q3BoundingBox_UnionPoint3D
• Q3BoundingBox_UnionRationalPoint4D
• Q3BoundingBox_SetFromPoints3D
• Q3BoundingBox_SetFromRationalPoints4D
• Managing Bounding Spheres
• Q3BoundingSphere_Copy
• Q3BoundingSphere_Union
• Q3BoundingSphere_Set
• Q3BoundingSphere_UnionPoint3D
• Q3BoundingSphere_UnionRationalPoint4D
• Q3BoundingSphere_SetFromPoints3D
• Q3BoundingSphere_SetFromRationalPoints4D