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M_VECTOR(3) Library Functions Manual M_VECTOR(3) NAME M_Vector -- Agar-Math vector-related functions SYNOPSIS #include <agar/core.h> #include <agar/gui.h> #include <agar/math/m.h> DESCRIPTION The M_Vector and M_Matrix(3) interfaces implement linear algebra operations on (real or complex valued) n dimensional vectors, and m by n matrices. Optimized interfaces are provided for fixed-dimensional types (which have entries directly accessible as x, y, z and w). Arbitrary-dimensional types may or may not use fixed arrays in memory. For example, the "sparse" back- end uses a sparse matrix representation, and the "db" backend stores vector entries in a database. Backends can be selected at run-time, or Agar-Math can be compiled to pro- vide inline expansions of all operations of a specific backend. Vector ex- tensions (such as SSE and AltiVec) are used by default, if a runtime cpuinfo check determines that they are available (the build remains compat- ible with non-vector platforms, at the cost of extra function calls). For best performance, Agar should be compiled with "--with-sse=inline", or "--with-altivec=inline". VECTORS IN R^N The following routines operate on dynamically-allocated vectors in R^n. Unlike M_Matrix (which might use different memory representations), vector entries are always directly accessible through the v array. The M_Vector structure is defined as: typedef struct m_vector { Uint m; /* Size */ M_Real *v; /* Elements */ } M_Vector; The following backends are currently available for M_Vector: fpu Native scalar floating point methods. VECTORS IN R^N: INITIALIZATION M_Vector * M_VecNew(Uint m) void M_VecFree(M_Vector *v) int M_VecResize(M_Vector *v, Uint m) void M_VecSetZero(M_Vector *v) M_Vector * M_ReadVector(AG_DataSource *ds) void M_WriteVector(AG_DataSource *ds, const M_Vector *v) The M_VecNew() function allocates a new vector in R^n. M_VecFree() re- leases all resources allocated for the specified vector. M_VecResize() resizes the vector v to m. Existing entries are preserved, but new entries are left uninitialized. If insufficient memory is avail- able, -1 is returned and an error message is set. On success, the function returns 0. M_VecSetZero() initializes v to the zero vector. M_ReadVector() reads a M_Vector from a data source and M_WriteVector() writes vector v to a data source; see AG_DataSource(3) for details. VECTORS IN R^N: ACCESSING ELEMENTS M_Real * M_VecGetElement(const M_Vector *v, Uint i) M_Real M_VecGet(const M_Vector *v, Uint i) M_Vector * M_VecFromReals(Uint n, const M_Real *values) M_Vector * M_VecFromFloats(Uint n, const float *values) M_Vector * M_VecFromDoubles(Uint n, const double *values) M_VecGetElement() returns a direct pointer to entry i in the (non-sparse) vector v. The M_VecGet() function returns the value of entry i in a vector v, which can be a sparse vector. M_VecFromReals(), M_VecFromFloats(), and M_VecFromDoubles() generate an M_Vector from an array of M_Real, float or double. VECTORS IN R^N: BASIC OPERATIONS int M_VecCopy(M_Vector *vDst, const M_Vector *vSrc) M_Vector * M_VecFlip(const M_Vector *v) M_Vector * M_VecScale(const M_Vector *v, M_Real c) void M_VecScalev(M_Vector *v, M_Real c) M_Vector * M_VecAdd(const M_Vector *a, const M_Vector *b) int M_VecAddv(M_Vector *a, const M_Vector *b) M_Vector * M_VecSub(const M_Vector *a, const M_Vector *b) int M_VecSubv(M_Vector *a, const M_Vector *b) M_Real M_VecLen(const M_Vector *v) M_Real M_VecDot(const M_Vector *a, const M_Vector *b) M_Real M_VecDistance(const M_Vector *a, const M_Vector *b) M_Vector * M_VecNorm(const M_Vector *v) M_Vector * M_VecLERP(const M_Vector *a, const M_Vector *b, M_Real t) M_Vector * M_VecElemPow(const M_Vector *v, M_Real pow) The M_VecCopy() routine copies the contents of vector vSrc into vDst. Both vectors must have the same size. The M_VecFlip() function returns the vector v scaled to -1. M_VecScale() scales the vector v by factor c and returns the resulting vec- tor. M_VecScalev() scales the vector in place. M_VecAdd() returns the sum of a and b, which must be of equal size. The M_VecAddv() variant writes the result back into a. M_VecSub() returns the difference (a - b). Both vectors must be of equal size. The M_VecSubv() variant writes the result back into a. M_VecLen() returns the Euclidean length of a vector. M_VecDot() returns the dot product of vectors a and b. M_VecDistance() returns the Euclidean distance between a and b. M_VecNorm() returns the normalized (unit-length) form of v. M_VecLERP() returns the result of linear interpolation between equally- sized vectors a and b, with scaling factor t. M_ElemPow() raises the entries of v to the power pow, and returns the re- sulting vector. VECTORS IN R^2 The following routines operate on vectors in R^2, which are always repre- sented by the structure: typedef struct m_vector2 { M_Real x, y; } M_Vector2; The following backends are currently available for M_Vector2: fpu Native scalar floating point methods. VECTORS IN R^2: INITIALIZATION M_Vector2 M_VecI2(void) M_Vector2 M_VecJ2(void) M_Vector2 M_VecZero2(void) M_Vector2 M_VecGet2(M_Real x, M_Real y) M_Vector2 M_VECTOR2(M_Real x, M_Real y) void M_VecSet2(M_Vector2 *v, M_Real x, M_Real y) void M_VecCopy2(M_Vector2 *vDst, const M_Vector2 *vSrc) M_Vector2 M_VecFromProj2(M_Vector3 p) M_Vector3 M_VecToProj2(M_Vector2 v, M_Real z) M_Vector2 M_ReadVector2(AG_DataSource *ds) void M_WriteVector2(AG_DataSource *ds, const M_Vector2 *v) The M_VecI2() and M_VecJ2() routines return the basis vectors [1;0] and [0;1], respectively. M_VecZero2() returns the zero vector [0;0]. M_VecGet2() returns the vector [x,y]. The M_VECTOR2() macro expands to a static initializer for the vector [x,y]. M_VecSet2() writes the values [x,y] into vector v (note that entries are also directly accessible via the M_Vector2 structure). M_VecFromProj2() returns an Euclidean vector corresponding to p in projec- tive space. If p is at infinity, a fatal divide-by-zero condition is raised. M_VecToProj2() returns the vector in projective space correspond- ing to v in Euclidean space (if w=1), or v at infinity (if w=0). M_ReadVector2() reads a M_Vector2 from a data source and M_WriteVector2() writes vector v to a data source; see AG_DataSource(3) for details. VECTORS IN R^2: BASIC OPERATIONS int M_VecCopy2(M_Vector2 *vDst, const M_Vector2 *vSrc) M_Vector2 M_VecFlip2(M_Vector2 v) M_Real M_VecLen2(M_Vector2 v) M_Real M_VecLen2p(const M_Vector2 *v) M_Real M_VecDot2(M_Vector2 a, M_Vector2 b) M_Real M_VecDot2p(const M_Vector2 *a, const M_Vector2 *b) M_Real M_VecPerpDot2(M_Vector2 a, M_Vector2 b) M_Real M_VecPerpDot2p(const M_Vector2 *a, const M_Vector2 *b) M_Real M_VecDistance2(M_Vector2 a, M_Vector2 b) M_Real M_VecDistance2p(const M_Vector2 *a, const M_Vector2 *b) M_Vector2 M_VecNorm2(M_Vector2 v) M_Vector2 M_VecNorm2p(const M_Vector2 *v) void M_VecNorm2v(M_Vector2 *v) M_Vector2 M_VecScale2(M_Vector2 v, M_Real c) M_Vector2 M_VecScale2p(const M_Vector2 *v, M_Real c) void M_VecScale2v(M_Vector2 *v, M_Real c) M_Vector2 M_VecAdd2(M_Vector2 a, M_Vector2 b) M_Vector2 M_VecAdd2p(const M_Vector2 *a, const M_Vector2 *b) void M_VecAdd2v(M_Vector2 *a, const M_Vector2 *b) M_Vector2 M_VecSum2(const M_Vector2 *vs, Uint count) M_Vector2 M_VecSub2(M_Vector2 a, M_Vector2 b) M_Vector2 M_VecSub2p(const M_Vector2 *a, const M_Vector2 *b) void M_VecSub2v(M_Vector2 *a, const M_Vector2 *b) M_Vector2 M_VecAvg2(M_Vector2 a, M_Vector2 b) M_Vector2 M_VecAvg2p(const M_Vector2 *a, const M_Vector2 *b) M_Vector2 M_VecLERP2(M_Vector2 a, M_Vector2 b, M_Real t) M_Vector2 M_VecLERP2p(M_Vector2 *a, M_Vector2 *b, M_Real t) M_Vector2 M_VecElemPow2(M_Vector2 *v, M_Real pow) M_Real M_VecVecAngle2(M_Vector2 a, M_Vector2 b) The M_VecCopy2() function copies the contents of vector vSrc into vDst. The function M_VecFlip2() returns the vector scaled to -1. M_VecLen2() and M_VecLen2p() return the real length of vector v, that is Sqrt(x^2 + y^2). M_VecDot2() and M_VecDot2p() return the dot product of vectors a and b, that is (a.x*b.x + a.y*b.y). M_VecPerpDot2() and M_VecPerpDot2p() compute the "perp dot product" of a and b, which is (a.x*b.y - a.y*b.x). M_VecDistance2() and M_VecDistance2p() return the real distance between vectors a and b, that is the length of the difference vector (a - b). M_VecNorm2() and M_VecNorm2p() return the normalized (unit-length) form of v. The M_VecNorm2v() variant normalizes the vector in-place. M_VecScale2() and M_VecScale2p() multiplies vector v by scalar c and re- turns the result. The M_VecScale2v() variant scales the vector in-place. M_VecAdd2() and M_VecAdd2p() return the sum of vectors a and b. The M_VecAdd2v() variant returns the result back into a. The M_VecSum2() func- tion returns the vector sum of the count vectors in the vs array. M_VecSub2() and M_VecSub2p() return the difference of vectors (a-b). The M_VecSub2v() variant returns the result back into a. The M_VecAvg2() and M_VecAvg2p() routines compute the average of two vec- tors (a+b)/2. The functions M_VecLERP2() and M_VecLERP2p() interpolate linearly between vectors a and b, using the scaling factor t and returns the result. The result is computed as a+(b-a)*t. M_VecElemPow2() raises the entries of v to the power pow, and returns the resulting vector. M_VecVecAngle2() returns the angle (in radians) between vectors a and b, about the origin. VECTORS IN R^3 The following routines operate on vectors in R^3, which are represented by the structure: #ifdef HAVE_SSE typedef union m_vector3 { __m128 m128; struct { float x, y, z, _pad; }; } M_Vector3; #else typedef struct m_vector3 { M_Real x, y, z; } M_Vector3; #endif Notice that SIMD extensions force single-precision floats, regardless of the precision for which Agar-Math was built (if a 3-dimensional vector of higher precision is required, the general M_Vector type may be used). The following backends are currently available for M_Vector3: fpu Native scalar floating point methods. sse Accelerate operations using Streaming SIMD Extensions (SSE). sse3 Accelerate operations using SSE3 extensions. VECTORS IN R^3: INITIALIZATION M_Vector3 M_VecI3(void) M_Vector3 M_VecJ3(void) M_Vector3 M_VecK3(void) M_Vector3 M_VecZero3(void) M_Vector3 M_VecGet3(M_Real x, M_Real y, M_Real z) M_Vector3 M_VECTOR3(M_Real x, M_Real y, M_Real z) void M_VecSet3(M_Vector3 *v, M_Real x, M_Real y, M_Real z) void M_VecCopy3(M_Vector3 *vDst, const M_Vector3 *vSrc) M_Vector3 M_VecFromProj3(M_Vector4 p) M_Vector4 M_VecToProj3(M_Vector3 v, M_Real w) M_Vector3 M_ReadVector3(AG_DataSource *ds) void M_WriteVector3(AG_DataSource *ds, const M_Vector3 *v) The M_VecI3(), M_VecJ3() and M_VecK3() routines return the basis vectors [1;0;0], [0;1;0] and [0;0;1], respectively. M_VecZero3() returns the zero vector [0;0;0]. M_VecGet3() returns the vector [x,y,z]. The M_VECTOR3() macro expands to a static initializer for the vector [x,y,z]. M_VecSet3() writes the values [x,y,z] into vector v (note that entries are also directly accessible via the M_Vector3 structure). M_VecFromProj3() returns an Euclidean vector corresponding to the specified vector p in projective space. If p is at infinity, a fatal divide-by-zero condition is raised. M_ReadVector3() reads a M_Vector3 from a data source and M_WriteVector3() writes vector v to a data source; see AG_DataSource(3) for details. VECTORS IN R^3: BASIC OPERATIONS int M_VecCopy3(M_Vector3 *vDst, const M_Vector3 *vSrc) M_Vector3 M_VecFlip3(M_Vector3 v) M_Real M_VecLen3(M_Vector3 v) M_Real M_VecLen3p(const M_Vector3 *v) M_Real M_VecDot3(M_Vector3 a, M_Vector3 b) M_Real M_VecDot3p(const M_Vector3 *a, const M_Vector3 *b) M_Real M_VecDistance3(M_Vector3 a, M_Vector3 b) M_Real M_VecDistance3p(const M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecNorm3(M_Vector3 v) M_Vector3 M_VecNorm3p(const M_Vector3 *v) void M_VecNorm3v(M_Vector3 *v) M_Vector3 M_VecCross3(M_Vector3 a, M_Vector3 b) M_Vector3 M_VecCross3p(const M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecNormCross3(M_Vector3 a, M_Vector3 b) M_Vector3 M_VecNormCross3p(const M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecScale3(M_Vector3 v, M_Real c) M_Vector3 M_VecScale3p(const M_Vector3 *v, M_Real c) void M_VecScale3v(M_Vector3 *v, M_Real c) M_Vector3 M_VecAdd3(M_Vector3 a, M_Vector3 b) M_Vector3 M_VecAdd3p(const M_Vector3 *a, const M_Vector3 *b) void M_VecAdd3v(M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecSum3(const M_Vector3 *vs, Uint count) M_Vector3 M_VecSub3(M_Vector3 a, M_Vector3 b) M_Vector3 M_VecSub3p(const M_Vector3 *a, const M_Vector3 *b) void M_VecSub3v(M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecAvg3(M_Vector3 a, M_Vector3 b) M_Vector3 M_VecAvg3p(const M_Vector3 *a, const M_Vector3 *b) M_Vector3 M_VecLERP3(M_Vector3 a, M_Vector3 b, M_Real t) M_Vector3 M_VecLERP3p(M_Vector3 *a, M_Vector3 *b, M_Real t) M_Vector3 M_VecElemPow3(M_Vector3 *v, M_Real pow) void M_VecVecAngle3(M_Vector3 a, M_Vector3 b, M_Real *theta, M_Real *phi) The M_VecCopy3() function copies the contents of vector vSrc into vDst. The function M_VecFlip3() returns the vector scaled to -1. M_VecLen3() and M_VecLen3p() return the real length of vector v, that is Sqrt(x^2 + y^2 + z^2). M_VecDot3() and M_VecDot3p() return the dot product of vectors a and b, that is (a.x*b.x + a.y*b.y + a.z*b.z). M_VecDistance3() and M_VecDistance3p() return the real distance between vectors a and b, that is the length of the difference vector (a - b). M_VecNorm3() and M_VecNorm3p() return the normalized (unit-length) form of v. The M_VecNorm3v() variant normalizes the vector in-place. M_VecCross3() and M_VecCross3p() return the cross-product (also known as the "vector product" or "Gibbs vector product) of vectors a and b. M_VecNormCross3() and M_VecNormCross3() return the normalized cross-product of vectors a and b. This is a useful operation in computer graphics (e.g., for computing plane normals from the vertices of a triangle). M_VecScale3() and M_VecScale3p() multiplies vector v by scalar c and re- turns the result. The M_VecScale3v() variant scales the vector in-place. M_VecAdd3() and M_VecAdd3p() return the sum of vectors a and b. The M_VecAdd3v() variant returns the result back into a. The M_VecSum3() func- tion returns the vector sum of the count vectors in the vs array. M_VecSub3() and M_VecSub3p() return the difference of vectors (a-b). The M_VecSub3v() variant returns the result back into a. The M_VecAvg3() and M_VecAvg3p() routines compute the average of two vec- tors (a+b)/2. The functions M_VecLERP3() and M_VecLERP3p() interpolate linearly between vectors a and b, using the scaling factor t and returns the result. The result is computed as a+(b-a)*t. M_VecElemPow3() raises the entries of v to the power pow, and returns the resulting vector. M_VecVecAngle3() returns the two angles (in radians) between vectors a and b, about the origin. VECTORS IN R^4 The following routines operate on vectors in R^4, which are represented by the structure: #ifdef HAVE_SSE typedef union m_vector4 { __m128 m128; struct { float x, y, z, w; }; } M_Vector4; #else typedef struct m_vector4 { M_Real x, y, z, w; } M_Vector4; #endif Notice that SIMD extensions force single-precision floats, regardless of the precision for which Agar-Math was built (if a 4-dimensional vector of higher precision is required, the general M_Vector type may be used). The following backends are currently available for M_Vector4: fpu Native scalar floating point methods. sse Accelerate operations using Streaming SIMD Extensions (SSE). sse3 Accelerate operations using SSE3 extensions. VECTORS IN R^4: INITIALIZATION M_Vector4 M_VecI4(void) M_Vector4 M_VecJ4(void) M_Vector4 M_VecK4(void) M_Vector4 M_VecL4(void) M_Vector4 M_VecZero4(void) M_Vector4 M_VecGet4(M_Real x, M_Real y, M_Real z, M_Real w) M_Vector4 M_VECTOR4(M_Real x, M_Real y, M_Real z, M_Real w) void M_VecSet4(M_Vector4 *v, M_Real x, M_Real y, M_Real z, M_Real w) void M_VecCopy4(M_Vector4 *vDst, const M_Vector4 *vSrc) M_Vector4 M_ReadVector4(AG_DataSource *ds) void M_WriteVector4(AG_DataSource *ds, const M_Vector4 *v) The M_VecI4(), M_VecJ4(), M_VecK4() and M_VecL4() routines return the basis vectors [1;0;0;0], [0;1;0;0], [0;0;1;0] and [0;0;0;1], respectively. M_VecZero4() returns the zero vector [0;0;0;0]. M_VecGet4() returns the vector [x,y,z,w]. The M_VECTOR4() macro expands to a static initializer for the vector [x,y,z,w]. M_VecSet4() writes the values [x,y,z,w] into vector v (note that entries are also directly accessible via the M_Vector4 structure). M_ReadVector4() reads a M_Vector4 from a data source and M_WriteVector4() writes vector v to a data source; see AG_DataSource(4) for details. VECTORS IN R^4: BASIC OPERATIONS int M_VecCopy4(M_Vector4 *vDst, const M_Vector4 *vSrc) M_Vector4 M_VecFlip4(M_Vector4 v) M_Real M_VecLen4(M_Vector4 v) M_Real M_VecLen4p(const M_Vector4 *v) M_Real M_VecDot4(M_Vector4 a, M_Vector4 b) M_Real M_VecDot4p(const M_Vector4 *a, const M_Vector4 *b) M_Real M_VecDistance4(M_Vector4 a, M_Vector4 b) M_Real M_VecDistance4p(const M_Vector4 *a, const M_Vector4 *b) M_Vector4 M_VecNorm4(M_Vector4 v) M_Vector4 M_VecNorm4p(const M_Vector4 *v) void M_VecNorm4v(M_Vector4 *v) M_Vector4 M_VecScale4(M_Vector4 v, M_Real c) M_Vector4 M_VecScale4p(const M_Vector4 *v, M_Real c) void M_VecScale4v(M_Vector4 *v, M_Real c) M_Vector4 M_VecAdd4(M_Vector4 a, M_Vector4 b) M_Vector4 M_VecAdd4p(const M_Vector4 *a, const M_Vector4 *b) void M_VecAdd4v(M_Vector4 *a, const M_Vector4 *b) M_Vector4 M_VecSum4(const M_Vector4 *vs, Uint count) M_Vector4 M_VecSub4(M_Vector4 a, M_Vector4 b) M_Vector4 M_VecSub4p(const M_Vector4 *a, const M_Vector4 *b) void M_VecSub4v(M_Vector4 *a, const M_Vector4 *b) M_Vector4 M_VecAvg4(M_Vector4 a, M_Vector4 b) M_Vector4 M_VecAvg4p(const M_Vector4 *a, const M_Vector4 *b) M_Vector4 M_VecLERP4(M_Vector4 a, M_Vector4 b, M_Real t) M_Vector4 M_VecLERP4p(M_Vector4 *a, M_Vector4 *b, M_Real t) M_Vector4 M_VecElemPow4(M_Vector4 *v, M_Real pow) void M_VecVecAngle4(M_Vector4 a, M_Vector4 b, M_Real *phi1, M_Real *phi2, M_Real *phi3) The M_VecCopy4() function copies the contents of vector vSrc into vDst. The function M_VecFlip4() returns the vector scaled to -1. M_VecLen4() and M_VecLen4p() return the real length of vector v, that is Sqrt(x^2 + y^2 + z^2 + w^2). M_VecDot4() and M_VecDot4p() return the dot product of vectors a and b, that is (a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w). M_VecDistance4() and M_VecDistance4p() return the real distance between vectors a and b, that is the length of the difference vector (a - b). M_VecNorm4() and M_VecNorm4p() return the normalized (unit-length) form of v. The M_VecNorm4v() variant normalizes the vector in-place. M_VecScale4() and M_VecScale4p() multiplies vector v by scalar c and re- turns the result. The M_VecScale4v() variant scales the vector in-place. M_VecAdd4() and M_VecAdd4p() return the sum of vectors a and b. The M_VecAdd4v() variant returns the result back into a. The M_VecSum4() func- tion returns the vector sum of the count vectors in the vs array. M_VecSub4() and M_VecSub4p() return the difference of vectors (a-b). The M_VecSub4v() variant returns the result back into a. The M_VecAvg4() and M_VecAvg4p() routines compute the average of two vec- tors (a+b)/2. The functions M_VecLERP4() and M_VecLERP4p() interpolate linearly between vectors a and b, using the scaling factor t and returns the result. The result is computed as a+(b-a)*t. M_VecElemPow4() raises the entries of v to the power pow, and returns the resulting vector. M_VecVecAngle4() returns the three angles (in radians) between vectors a and b, about the origin. SEE ALSO AG_Intro(3), M_Complex(3), M_Matrix(3), M_Matview(3), M_Quaternion(3), M_Real(3) HISTORY The M_Vector interface first appeared in Agar 1.3.4. Agar 1.7 December 21, 2022 M_VECTOR(3)
NAME | SYNOPSIS | DESCRIPTION | VECTORS IN R^N | VECTORS IN R^N: INITIALIZATION | VECTORS IN R^N: ACCESSING ELEMENTS | VECTORS IN R^N: BASIC OPERATIONS | VECTORS IN R^2 | VECTORS IN R^2: INITIALIZATION | VECTORS IN R^2: BASIC OPERATIONS | VECTORS IN R^3 | VECTORS IN R^3: INITIALIZATION | VECTORS IN R^3: BASIC OPERATIONS | VECTORS IN R^4 | VECTORS IN R^4: INITIALIZATION | VECTORS IN R^4: BASIC OPERATIONS | SEE ALSO | HISTORY
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