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95 lines
2.4 KiB
C
95 lines
2.4 KiB
C
#include "four_point_transform.h"
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#include "singular_value_decomposition.h"
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/* Make a 4x4 matrix that maps
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* e1 -> p1
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* e2 -> p3
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* e3 -> p3
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* (1,1,1,0) -> p4
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*/
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static void
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unit_to (graphene_point3d_t *p1,
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graphene_point3d_t *p2,
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graphene_point3d_t *p3,
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graphene_point3d_t *p4,
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graphene_matrix_t *m)
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{
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graphene_vec3_t v1, v2, v3, v4;
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graphene_vec4_t vv1, vv2, vv3, vv4, p;
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graphene_matrix_t u, s;
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float v[16] = { 0., };
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double A[16];
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double U[16];
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double S[4];
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double V[16];
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double B[4];
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double x[4];
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int i, j;
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graphene_point3d_to_vec3 (p1, &v1);
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graphene_point3d_to_vec3 (p2, &v2);
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graphene_point3d_to_vec3 (p3, &v3);
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graphene_point3d_to_vec3 (p4, &v4);
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graphene_vec4_init_from_vec3 (&vv1, &v1, 1.);
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graphene_vec4_init_from_vec3 (&vv2, &v2, 1.);
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graphene_vec4_init_from_vec3 (&vv3, &v3, 1.);
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graphene_vec4_init_from_vec3 (&vv4, &v4, 1.);
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graphene_vec4_init (&p, 0., 0., 0., 1.);
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graphene_matrix_init_from_vec4 (&u, &vv1, &vv2, &vv3, &p);
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/* solve x * u = vv4 */
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for (i = 0; i < 4; i++)
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for (j = 0; j < 4; j++)
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A[j * 4 + i] = graphene_matrix_get_value (&u, i, j);
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B[0] = graphene_vec4_get_x (&vv4);
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B[1] = graphene_vec4_get_y (&vv4);
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B[2] = graphene_vec4_get_z (&vv4);
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B[3] = graphene_vec4_get_w (&vv4);
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singular_value_decomposition (A, 4, 4, U, S, V);
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singular_value_decomposition_solve (U, S, V, 4, 4, B, x);
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v[ 0] = x[0];
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v[ 5] = x[1];
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v[10] = x[2];
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v[15] = 1;
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graphene_matrix_init_from_float (&s, (const float *)&v);
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graphene_matrix_multiply (&s, &u, m);
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}
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/* Compute a 4x4 matrix m that maps
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* p1 -> q1
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* p2 -> q2
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* p3 -> q3
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* p4 -> q4
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*
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* This is not in general possible, because projective
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* transforms preserve coplanarity. But in the cases we
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* care about here, both sets of points are always coplanar.
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*/
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void
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perspective_3d (graphene_point3d_t *p1,
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graphene_point3d_t *p2,
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graphene_point3d_t *p3,
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graphene_point3d_t *p4,
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graphene_point3d_t *q1,
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graphene_point3d_t *q2,
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graphene_point3d_t *q3,
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graphene_point3d_t *q4,
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graphene_matrix_t *m)
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{
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graphene_matrix_t a, a_inv, b;
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unit_to (p1, p2, p3, p4, &a);
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unit_to (q1, q2, q3, q4, &b);
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graphene_matrix_inverse (&a, &a_inv);
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graphene_matrix_multiply (&a_inv, &b, m);
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}
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