pfVec3 - Set and operate on 3-component vectors
void* pfVec3::operator new(size_t);
void* pfVec3::operator new(size_t, void *arena);
void pfVec3::add(const pfVec3& v1, const pfVec3& v2);
int pfVec3::equal(const pfVec3& v2);
int pfVec3::almostEqual(const pfVec3& v2, float tol);
void pfVec3::copy(const pfVec3& v);
void pfVec3::cross(const pfVec3& v1, const pfVec3& v2);
float pfVec3::distance(const pfVec3& pt2);
float pfVec3::dot(const pfVec3& v2);
float pfVec3::length(void);
void pfVec3::negate(const pfVec3& v);
float pfVec3::normalize(void);
void pfVec3::scale(float s, const pfVec3& v);
void pfVec3::set(float x, float y, float z);
float pfVec3::sqrDistance(const pfVec3& pt2);
void pfVec3::sub(const pfVec3& v1, const pfVec3& v2);
void pfVec3::xformVec(const pfVec3& v, const pfMatrix& m);
void pfVec3::xformPt(const pfVec3& v, const pfMatrix& m);
void pfVec3::fullXformPt(const pfVec3& v, const pfMatrix& m);
float& pfVec3::operator [](int i);
const float& pfVec3::operator [](int i);
int pfVec3::operator ==(const pfVec3& v);
pfVec3 pfVec3::operator -() const;
pfVec3 pfVec3::operator +(const pfVec3& v);
pfVec3 pfVec3::operator -(const pfVec3& v);
pfVec3& pfVec3::operator =(const pfVec3& v);
pfVec3& pfVec3::operator *=(float d);
pfVec3& pfVec3::operator /=(float d);
pfVec3& pfVec3::operator +=(const pfVec3& v);
pfVec3& pfVec3::operator -=(const pfVec3& v);
pfVec3 pfVec3::operator *(const pfVec3& v, float d);
pfVec3 pfVec3::operator *(float d, const pfVec3& v);
pfVec3 pfVec3::operator /(const pfVec3& v, float d);
pfVec3 pfVec3::operator *(const pfVec3& v, const pfMatrix& m);
struct pfVec3 {
float vec[3];
};
Math functions for 3-component vectors. Most of these routines have macro equivalents.
Most accesses to pfVec3 go through pfVec3::operator[], but pfVec3 is a public struct whose data member vec is directly accessible, e.g. when necessary for passing to a routine expecting a float* such as glColor3fv. The default constructor pfVec3() is empty and does not initialize the values in the vector. An initializing constructor pfVec3(float, float, float) accepts the initial values for the vector. new(arena) allocates a pfVec3 from the specified memory arena, or from the heap if arena is
NULL. new allocates a pfVec3 from the default memory arena (- pfGetSharedArena). pfVec3s can also be created automatically on the stack or statically. pfVec3s allocated with new can should be deleted with pfDelete, not delete.
The name vec has been used below to indicate the pfVec3 on which the member function is being invoked.
pfVec3::set: vec[0] = x, vec[1] = y, vec[2] = z. Macro equivalent is PFSET_VEC3.
pfVec3::copy: vec = v. Macro equivalent is PFCOPY_VEC3.
pfVec3::negate: vec = -v. Macro equivalent is PFNEGATE_VEC3.
pfVec3::add: vec = v1 + v2. Sets vec to the sum of vectors v1 and v2. Macro equivalent is PFADD_VEC3.
pfVec3::sub: vec = v1 - v2. Sets vec to the difference of v1 and v2.
Macro equivalent is PFSUB_VEC3.
pfVec3::scale: vec = s * v1. Sets vec to the vector v scaled by s.
Macro equivalent is PFSCALE_VEC3.
pfVec3::addScaled: vec = v1 + s * v2. Sets vec to the vector v1 plus the
vector v2 scaled by s. Macro equivalent is PFADD_SCALED_VEC3.
pfVec3::combine: vec = s1 * v1 + s2 * v2. Sets vec to be the linear combination of v1 and v2 with scales s1 and s2, respectively. Macro equivalent: PFCOMBINE_VEC3.
pfVec3::normalize: vec = vec / length(vec). Normalizes the vector vec to have unit length and returns the original length of the vector.
pfVec3::cross: vec = v1 X v2. Sets vec to the cross-product of two vectors v1 and v2.
pfVec3::xformVec: vec = v * m (vec[i]=v[i] i=0, 1, 2; v[3] = 0). Transforms v as a vector by the matrix m.
pfVec3::xformPt: vec = vec * m (vec[i]=vec[i] i=0, 1, 2; vec[3] = 1). Transforms vec as a point by the matrix m using the 4X3 submatrix.
pfVec3::fullXformPt: vec = v * m (vec[i]=v[i] i=0, 1, 2; vec[3] = 1). Transforms vec as a point by the matrix m using the full 4X4 matrix and scaling dst by the resulting w coordinate.
pfVec3::dot = vec dot v2 = vec[0] * v2[0] + vec[1] * v2[1] + vec[2] *
v2[2]. Returns dot product of the vectors vec and v2. Macro equivalent
is PFDOT_VEC3.
vec. Macro equivalent is PFLENGTH_VEC3.
pfVec3::sqrDistance = (vec - v2) dot (vec - v2). Returns square of distance between two points vec and v2. Macro equivalent is PFSQR_DISTANCE_PT3.
pfVec3::distance = sqrt((vec - v2) dot (vec - v2)). Returns distance
between two points vec and v2. Macro equivalent is PFDISTANCE_PT3.
pfVec3::equal = (vec == v2). Tests for strict component-wise equality of two vectors vec and v2 and returns FALSE or TRUE. Macro equivalent is PFEQUAL_VEC3.
pfVec3::almostEqual. Tests for approximate component-wise equality of
two vectors vec and v2. It returns FALSE or TRUE depending on whether
the absolute value of the difference between each pair of components is
less than the tolerance tol. Macro equivalent is PFALMOST_EQUAL_VEC3.
float& operator [](int) const float& operator [](int) Accesses indexed component of vector.
pfVec3 operator -() const Nondestructive unary negation - returns a new vector.
pfVec3 operator +(const pfVec3&) pfVec3 operator -(const pfVec3&) Component-wise binary vector addition and subtraction operators.
pfVec3& operator *=(float) pfVec3& operator /=(float) Component-wise scalar multiplication and division operators.
pfVec3& operator +=(const pfVec3&) pfVec3& operator -=(const pfVec3&) Component-wise vector addition and subtraction operators.
pfVec3 operator *(const pfVec3&, float) pfVec3 operator *(float d, const pfVec3&) pfVec3 operator /(const pfVec3&, float) pfVec3 operator *(const pfVec3&, const pfMatrix&) Component-wise binary scalar multiplication and division operators.
Routines can accept the same vector as source, destination, or as a repeated operand.
When using overloaded operators in C++, assignment operators, e.g. "+=", are somewhat more efficient than the corresponding binary operators, e.g. "+", because the latter construct a temporary intermediate object. Use assignment operators or macros for binary operations where optimal speed is important.
C++ does not support array deletion (i.e. delete[]) for arrays of objects allocated new operators that take additional arguments. Hence, the array deletion operator delete[] should not be used on arrays of objects created with new(arena) pfVec3[n].
pfMatrix, pfVec2, pfVec4
pfAddScaledVec3, pfAddVec3, pfEqualVec3, pfAlmostEqualVec3, pfCombineVec3, pfCopyVec3, pfCrossVec3, pfDistancePt3, pfDotVec3, pfLengthVec3, pfNegateVec3, pfNormalizeVec3, pfScaleVec3, pfSetVec3, pfSqrDistancePt3, pfSubVec3, pfXformVec3, pfXformPt3, pfFullXformPt3 - Set and operate on 3-component vectors
void pfAddVec3(pfVec3 dst, const pfVec3 v1, const pfVec3 v2);
int pfEqualVec3(const pfVec3 v1, const pfVec3 v2);
int pfAlmostEqualVec3(const pfVec3 v1, const pfVec3 v2, float tol);
void pfCopyVec3(pfVec3 dst, const pfVec3 v);
void pfCrossVec3(pfVec3 dst, const pfVec3 v1, const pfVec3 v2);
float pfDistancePt3(const pfVec3 pt1, const pfVec3 pt2);
float pfDotVec3(const pfVec3 v1, const pfVec3 v2);
float pfLengthVec3(const pfVec3 v);
void pfNegateVec3(pfVec3 dst, const pfVec3 v);
float pfNormalizeVec3(pfVec3 v);
void pfScaleVec3(pfVec3 dst, float s, const pfVec3 v);
void pfSetVec3(pfVec3 dst, float x, float y, float z);
float pfSqrDistancePt3(const pfVec3 pt1, const pfVec3 pt2);
void pfSubVec3(pfVec3 dst, const pfVec3 v1, const pfVec3 v2);
void pfXformVec3(pfVec3 dst, const pfVec3 v, const pfMatrix m);
void pfXformPt3(pfVec3 dst, const pfVec3 v, const pfMatrix m);
void pfFullXformPt3(pfVec3 dst, const pfVec3 v, const pfMatrix m);
Math functions for 3-component vectors. Most of these routines have macro equivalents.
pfSetVec3(dst, x, y, z): dst[0] = x, dst[1] = y, dst[2] = z. Macro
equivalent is PFSET_VEC3.
pfCopyVec3(dst, v): dst = v. Macro equivalent is PFCOPY_VEC3.
pfNegateVec3(dst, v): dst = -v. Macro equivalent is PFNEGATE_VEC3.
pfAddVec3(dst, v1, v2): dst = v1 + v2. Sets dst to the sum of vectors v1 and v2. Macro equivalent is PFADD_VEC3.
pfSubVec3(dst, v1, v2): dst = v1 - v2. Sets dst to the difference of v1
and v2. Macro equivalent is PFSUB_VEC3.
pfScaleVec3(dst, s, v): dst = s * v1. Sets dst to the vector v scaled by
s. Macro equivalent is PFSCALE_VEC3.
pfAddScaledVec3(dst, v1, s, v2): dst = v1 + s * v2. Sets dst to the vector v1 plus the vector v2 scaled by s. Macro equivalent is PFADD_SCALED_VEC3.
pfCombineVec3(dst, s1, v1, s2, v2): dst = s1 * v1 + s2 * v2. Sets dst to be the linear combination of v1 and v2 with scales s1 and s2, respectively. Macro equivalent: PFCOMBINE_VEC3.
pfNormalizeVec3(v): v = v / length(v). Normalizes the vector v to have unit length and returns the original length of the vector.
pfCrossVec3(dst, v1, v2): dst = v1 X v2. Sets dst to the cross-product of two vectors v1 and v2.
pfXformVec3(dst, v, m): dst = v4 * m (v4[i]=v[i] i=0, 1, 2; v4[3] = 0). Transforms v as a vector by the matrix m.
pfXformPt3(dst, v, m): dst = v4 * m (v4[i]=v[i] i=0, 1, 2; v4[3] = 1). Transforms v as a point by the matrix m using the 4X3 submatrix.
pfFullXformPt3(dst, v, m): dst = v4 * m (v4[i]=v[i] i=0, 1, 2; v4[3] = 1). Transforms v as a point by the matrix m using the full 4X4 matrix and scaling dst by the resulting w coordinate.
pfDotVec3(v1, v2) = v1 dot v2 = v1[0] * v2[0] + v1[1] * v2[1] + v1[2] *
v2[2]. Returns dot product of the vectors v1 and v2. Macro equivalent
is PFDOT_VEC3.
pfLengthVec3(v) = |v| = sqrt(v dot v). Returns length of the vector v.
Macro equivalent is PFLENGTH_VEC3.
pfSqrDistancePt3(v1, v2) = (v1 - v2) dot (v1 - v2). Returns square of distance between two points v1 and v2. Macro equivalent is PFSQR_DISTANCE_PT3.
pfDistancePt3(v1, v2) = sqrt((v1 - v2) dot (v1 - v2)). Returns distance
between two points v1 and v2. Macro equivalent is PFDISTANCE_PT3.
pfEqualVec3(v1, v2) = (v1 == v2). Tests for strict component-wise
equality of two vectors v1 and v2 and returns FALSE or TRUE. Macro
equivalent is PFEQUAL_VEC3.
pfAlmostEqualVec3(v1, v2, tol). Tests for approximate component-wise equality of two vectors v1 and v2. It returns FALSE or TRUE depending on whether the absolute value of the difference between each pair of components is less than the tolerance tol. Macro equivalent is PFALMOST_EQUAL_VEC3.
Routines can accept the same vector as source, destination, or as a repeated operand.
pfMatrix, pfVec2, pfVec4