| | | GTS Library Reference Manual | |
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#include <gts.h> typedef GtsVector[3]; typedef GtsVector4[4]; #define gts_vector_init (v, p1, p2) #define gts_vector_scalar (v1, v2) #define gts_vector_cross (C,A,B) #define gts_vector_norm (v) #define gts_vector_normalize (v) void gts_vector_print (GtsVector v,FILE *fptr); void gts_vector4_print (GtsVector4 v,FILE *fptr); typedef GtsMatrix; GtsMatrix* gts_matrix_new (gdouble a00,gdouble a01,gdouble a02,gdouble a03,gdouble a10,gdouble a11,gdouble a12,gdouble a13,gdouble a20,gdouble a21,gdouble a22,gdouble a23,gdouble a30,gdouble a31,gdouble a32,gdouble a33); void gts_matrix_assign (GtsMatrix *m,gdouble a00,gdouble a01,gdouble a02,gdouble a03,gdouble a10,gdouble a11,gdouble a12,gdouble a13,gdouble a20,gdouble a21,gdouble a22,gdouble a23,gdouble a30,gdouble a31,gdouble a32,gdouble a33); GtsMatrix* gts_matrix_zero (GtsMatrix *m); GtsMatrix* gts_matrix_identity (GtsMatrix *m); GtsMatrix* gts_matrix_projection (GtsTriangle *t); GtsMatrix* gts_matrix_scale (GtsMatrix *m,GtsVector s); GtsMatrix* gts_matrix_translate (GtsMatrix *m,GtsVector t); GtsMatrix* gts_matrix_rotate (GtsMatrix *m,GtsVector r,gdouble angle); GtsMatrix* gts_matrix_transpose (GtsMatrix *m);gdouble gts_matrix_determinant (GtsMatrix *m); GtsMatrix* gts_matrix_inverse (GtsMatrix *m); GtsMatrix* gts_matrix3_inverse (GtsMatrix *m); GtsMatrix* gts_matrix_product (GtsMatrix *m1, GtsMatrix *m2);guint gts_matrix_compatible_row (GtsMatrix *A,GtsVector b,guint n,GtsVector A1,gdouble b1);guint gts_matrix_quadratic_optimization (GtsMatrix *A,GtsVector b,guint n, GtsMatrix *H,GtsVector c); void gts_matrix_print (GtsMatrix *m,FILE *fptr); void gts_matrix_destroy (GtsMatrix *m);
The functions described in this section allow to perform simple transformations on point coordinates. In particular projection onto a plane passing through the vertices of a given triangle or quadratic optimization problems.
#define gts_vector_init(v, p1, p2)
Given two points p1 and p2, fills v with the coordinates of vector p1->p2.
| v : | a |
| p1 : | a GtsPoint. |
| p2 : | another GtsPoint. |
#define gts_vector_scalar(v1, v2)
Given two vectors v1 and v2 evaluates to the scalar product v1.v2.
| v1 : | a |
| v2 : | another |
#define gts_vector_cross(C,A,B)
Given two vectors A and B fills C with the coordinates of the cross-product A^B.
| C : | a |
| A : | another |
| B : | and another. |
void gts_vector_print (GtsVector v,FILE *fptr);
Print s to file fptr.
| v : | a |
| fptr : | a file descriptor. |
void gts_vector4_print (GtsVector4 v,FILE *fptr);
Print v to file fptr.
| v : | a |
| fptr : | a file descriptor. |
GtsMatrix* gts_matrix_new (gdouble a00,gdouble a01,gdouble a02,gdouble a03,gdouble a10,gdouble a11,gdouble a12,gdouble a13,gdouble a20,gdouble a21,gdouble a22,gdouble a23,gdouble a30,gdouble a31,gdouble a32,gdouble a33);
Allocates memory and initializes a new GtsMatrix.
| a00 : | element [0][0]. |
| a01 : | element [0][1]. |
| a02 : | element [0][2]. |
| a03 : | element [0][3]. |
| a10 : | element [1][0]. |
| a11 : | element [1][1]. |
| a12 : | element [1][2]. |
| a13 : | element [1][3]. |
| a20 : | element [2][0]. |
| a21 : | element [2][1]. |
| a22 : | element [2][2]. |
| a23 : | element [2][3]. |
| a30 : | element [3][0]. |
| a31 : | element [3][1]. |
| a32 : | element [3][2]. |
| a33 : | element [3][3]. |
| Returns : | a pointer to the newly created GtsMatrix. |
void gts_matrix_assign (GtsMatrix *m,gdouble a00,gdouble a01,gdouble a02,gdouble a03,gdouble a10,gdouble a11,gdouble a12,gdouble a13,gdouble a20,gdouble a21,gdouble a22,gdouble a23,gdouble a30,gdouble a31,gdouble a32,gdouble a33);
Set values of matrix elements.
| m : | a GtsMatrix. |
| a00 : | element [0][0]. |
| a01 : | element [0][1]. |
| a02 : | element [0][2]. |
| a03 : | element [0][3]. |
| a10 : | element [1][0]. |
| a11 : | element [1][1]. |
| a12 : | element [1][2]. |
| a13 : | element [1][3]. |
| a20 : | element [2][0]. |
| a21 : | element [2][1]. |
| a22 : | element [2][2]. |
| a23 : | element [2][3]. |
| a30 : | element [3][0]. |
| a31 : | element [3][1]. |
| a32 : | element [3][2]. |
| a33 : | element [3][3]. |
GtsMatrix* gts_matrix_zero (GtsMatrix *m);
Initializes m to zeros. Allocates a matrix if m is NULL.
| m : | a GtsMatrix or $NULL. |
| Returns : | the zero'ed matrix. |
GtsMatrix* gts_matrix_identity (GtsMatrix *m);
Initializes m to an identity matrix. Allocates a matrix if m is NULL.
| m : | a GtsMatrix or NULL. |
| Returns : | the identity matrix. |
GtsMatrix* gts_matrix_projection (GtsTriangle *t);
Creates a new GtsMatrix representing the projection onto a plane of normal given by t.
| t : | a GtsTriangle. |
| Returns : | a pointer to the newly created GtsMatrix. |
GtsMatrix* gts_matrix_scale (GtsMatrix *m,GtsVector s);
Initializes m to a scaling matrix for s. Allocates a matrix if m is NULL.
| m : | a GtsMatrix or NULL. |
| s : | the scaling vector. |
| Returns : | the scaling matrix. |
GtsMatrix* gts_matrix_translate (GtsMatrix *m,GtsVector t);
Initializes m to a translation matrix for t. Allocates a new matrix if m is NULL.
| m : | a GtsMatrix or NULL. |
| t : | the translation vector. |
| Returns : | the translation matix. |
GtsMatrix* gts_matrix_rotate (GtsMatrix *m,GtsVector r,gdouble angle);
Initializes m to a rotation matrix around r by angle. Allocates a new matrix if m is NULL.
| m : | a GtsMatrix or NULL. |
| r : | the rotation axis. |
| angle : | the angle (in radians) to rotate by. |
| Returns : | the rotation matrix. |
GtsMatrix* gts_matrix_transpose (GtsMatrix *m);
| m : | a GtsMatrix. |
| Returns : | a pointer to a newly created GtsMatrix transposed of m. |
gdouble gts_matrix_determinant (GtsMatrix *m);
| m : | a GtsMatrix. |
| Returns : | the value of det(m). |
GtsMatrix* gts_matrix_inverse (GtsMatrix *m);
| m : | a GtsMatrix. |
| Returns : | a pointer to a newly created GtsMatrix inverse of m or NULL if m is not invertible. |
GtsMatrix* gts_matrix3_inverse (GtsMatrix *m);
| m : | a 3x3 GtsMatrix. |
| Returns : | a pointer to a newly created 3x3 GtsMatrix inverse of m or NULL if m is not invertible. |
GtsMatrix* gts_matrix_product (GtsMatrix *m1, GtsMatrix *m2);
| m1 : | a GtsMatrix. |
| m2 : | another GtsMatrix. |
| Returns : | a new GtsMatrix, product of m1 and m2. |
guint gts_matrix_compatible_row (GtsMatrix *A,GtsVector b,guint n,GtsVector A1,gdouble b1);
Given a system of n constraints A.x=b adds to it the compatible constraints defined by A1.x=b1. The compatibility is determined by insuring that the resulting system is well-conditioned (see Lindstrom and Turk (1998, 1999)).
| A : | a GtsMatrix. |
| b : | a |
| n : | the number of previous constraints of A.x=b. |
| A1 : | a GtsMatrix. |
| b1 : | a |
| Returns : | the number of constraints of the resulting system. |
guint gts_matrix_quadratic_optimization (GtsMatrix *A,GtsVector b,guint n, GtsMatrix *H,GtsVector c);
Solve a quadratic optimization problem: Given a quadratic objective function f which can be written as: f(x) = x^t.H.x + c^t.x + k, where H is the symmetric positive definite Hessian of f and k is a constant, find the minimum of f subject to the set of n prior linear constraints, defined by the first n rows of A and b (A.x = b). The new constraints given by the minimization are added to A and b only if they are linearly independent as determined by gts_matrix_compatible_row().
| A : | a GtsMatrix. |
| b : | a |
| n : | the number of constraints (must be smaller than 3). |
| H : | a symmetric positive definite Hessian. |
| c : | a |
| Returns : | the new number of constraints defined by A and b. |
void gts_matrix_print (GtsMatrix *m,FILE *fptr);
Print m to file fptr.
| m : | a GtsMatrix. |
| fptr : | a file descriptor. |
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