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vector.h
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1992-06-16
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/***********************************************************************
* The following macros handle most vector operations, the exceptions
* usually being complex equations with four or more vectors.
*
* An alternate form for the multiple-statement macros is the
* "if (1) <macro_body> else" form. This allows for temporary variable
* declaration and control-flow constructs, but cannot be used
* everywhere a function call could, as with the form used below.
*
* Note that since the vector arguments are not enclosed in parentheses
* in the macro body, you can scale the vector arguments in the macro
* calls, e.g. Vec2Op(vec1,=,scalar*vec2).
*
* Here are some example uses of the following macros:
*
* printf ("Vector = <%lg %lg %lg>\n", VecList(vector))
* vector_dot = VecDot (vec1, vec2)
* norm = VecNorm (vector)
* VecScalar (vector, /=, norm)
* VecScalar (vector, *=, scale)
* Vec3Scalar (Xaxis, =, 1.0, 0.0, 0.0)
* Vec3Scalar (vector, *=, Xshear, Yshear, Zshear)
* Vec2Op (vector, =, Xaxis)
* Vec2Op (vector, +=, norm * Xaxis)
* Vec3Op (vec1, =, vec2, =, Xaxis)
* Vec3Op (vec1, =, vec2, -, vec3)
* Vec3Op (vec1, +=, scale2 * vec2, -, scale3 * vec3)
* VecCross (vec1, -=, vec2, X, vec3)
* VecCrossSafe (vec1, =, vec1, X, Xaxis)
***********************************************************************/
#include <math.h> /* Needed for sqrt() definition. */
/* Vector type definition. If you define colors in the same manner,
** you can also use these macros for color vector operations. */
typedef long float Vector[3];
typedef Vector Point; /* For readability. */
/* VecList enumerates the vector fields for function calls. */
#define VecList(V) V[0], V[1], V[2]
/* This macro computes the dot product of two vectors. */
#define VecDot(A,B) ((A[0]*B[0]) + (A[1]*B[1]) + (A[2]*B[2]))
/* The VecNorm macro computes the norm of the vector. */
#define VecNorm(V) sqrt(VecDot(V,V))
/* VecScalar provides for scalar operations on a vector. */
#define VecScalar(V,assign_op,k) \
( V[0] assign_op k, \
V[1] assign_op k, \
V[2] assign_op k \
)
/* Vec3Scalar provides for vector operations that involve three
** distinct scalar factors. */
#define Vec3Scalar(V,assign_op,a,b,c) \
( V[0] assign_op a, \
V[1] assign_op b, \
V[2] assign_op c \
)
/* Vec2Op provides for operations with two vectors. */
#define Vec2Op(A,assign_op,B) \
( A[0] assign_op B[0], \
A[1] assign_op B[1], \
A[2] assign_op B[2] \
)
/* Vec3op handles vector operations with three vectors. */
#define Vec3Op(A,assign_op,B,op,C) \
( A[0] assign_op B[0] op C[0], \
A[1] assign_op B[1] op C[1], \
A[2] assign_op B[2] op C[2] \
)
/* The cross product macros come in two flavors. VecCross() requires
** that all three vectors are distinct. With the VecCrossSafe()
** macro, it's OK to do A <- A X B, but this requires a temporary
** vector for storage, which in turn requires the "if (1) ... else"
** form. As an alternative, a global temporary vector could be used.
*/
#define VecCross(A,assign_op,B,dummy_op,C) \
( A[0] assign_op (B[1] * C[2]) - (B[2] * C[1]), \
A[1] assign_op (B[2] * C[0]) - (B[0] * C[2]), \
A[2] assign_op (B[0] * C[1]) - (B[1] * C[0]) \
)
#define VecCrossSafe(A,assign_op,B,dummy_op,C) \
if (1) \
{ auto Vector result; \
VecCross (result,=,B,X,C); \
Vec2Op (A,=,result); \
} else