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cogl/matrix: Calculate inverse using graphene matrices
Turns out inverting a matrix was the largest chunk of the CoglMatrix code. By switching to Graphene, a lot of it can go away. The inverse is still cached in the CoglMatrix struct itself, to preserve the optimization. However, switching to graphene_matrix_t to calculate the inverse has a challenge: float precision. We had to work around it here, and it needs an explanation. The way to detect whether a matrix is invertible or not (i.e. whether it's not a "singular" matrix, or not) is by checking if the determinant equals 0. So far, so good. Both graphene_matrix_t and CoglMatrix use single-precision floats to store their 4x4 matrices. Graphene uses vectorized operations to optimize determinant calculation, while Cogl tries to keep track of the matrix type and has special-purpose determinant functions for different matrix types (the most common one being a 3D matrix). Cogl, however, has a fundamentally flawed check for whether the matrix is invertible or not. Have a look: ``` float det; … if (det*det < 1e-25) return FALSE; ``` Notice that 1e-25 is *way* smaller than FLT_EPSILON. This check is fundamentally flawed. "In practice, what does it break?", the reader might ask. Well, in this case, the answer is opposite of that: Cogl inverts matrices that should not be invertible. Let's see an example: the model-view-projection of a 4K monitor. It looks like this: ``` | +0,002693 +0,000000 +0,000000 +0,000000 | | +0,000000 -0,002693 +0,000000 +0,000000 | | +0,000000 +0,000000 +0,002693 +0,000000 | | -5,169809 +2,908017 -5,036834 +1,000000 | ``` The determinant of this matrix is -0.000000019530306557. It evidently is smaller than FLT_EPSILON. In this situation, Cogl would happily calculate the inverse matrix, whereas Graphene (correctly) bails out and thinks it's a singular matrix. This commit works around that by exploiting the maths around it. The basis of it is: inverse(scalar * M) = (1/scalar) * M' which can be extrapolated to: inverse(M) = scalar * inverse(scalar * M) = M' In other words, scaling the to-be-inversed matrix, then scaling the inverse matrix by the same factor, gives us the desired inverse. In this commit, the scale is calculated as 1 / (smallest value in the diagonal). I'm sorry for everyone that has to read through this :( https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/1439
This commit is contained in:
Georges Basile Stavracas Neto
parent
cb733f8fbc
commit
ada5e67f7e
@ -112,28 +112,6 @@ enum CoglMatrixType {
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COGL_MATRIX_N_TYPES
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COGL_MATRIX_N_TYPES
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} ;
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} ;
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#define DEG2RAD (G_PI/180.0)
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/* Dot product of two 2-element vectors */
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#define DOT2(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] )
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/* Dot product of two 3-element vectors */
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#define DOT3(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] )
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#define CROSS3(N, U, V) \
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do { \
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(N)[0] = (U)[1]*(V)[2] - (U)[2]*(V)[1]; \
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(N)[1] = (U)[2]*(V)[0] - (U)[0]*(V)[2]; \
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(N)[2] = (U)[0]*(V)[1] - (U)[1]*(V)[0]; \
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} while (0)
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#define SUB_3V(DST, SRCA, SRCB) \
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do { \
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(DST)[0] = (SRCA)[0] - (SRCB)[0]; \
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(DST)[1] = (SRCA)[1] - (SRCB)[1]; \
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(DST)[2] = (SRCA)[2] - (SRCB)[2]; \
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} while (0)
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#define LEN_SQUARED_3FV( V ) ((V)[0]*(V)[0]+(V)[1]*(V)[1]+(V)[2]*(V)[2])
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#define LEN_SQUARED_3FV( V ) ((V)[0]*(V)[0]+(V)[1]*(V)[1]+(V)[2]*(V)[2])
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/*
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/*
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@ -337,686 +315,6 @@ cogl_debug_matrix_print (const CoglMatrix *matrix)
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*/
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*/
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#define MAT(m,r,c) (m)[(c)*4+(r)]
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#define MAT(m,r,c) (m)[(c)*4+(r)]
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/*
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* Swaps the values of two floating pointer variables.
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*
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* Used by invert_matrix_general() to swap the row pointers.
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*/
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#define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
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/*
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* Compute inverse of 4x4 transformation matrix.
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*
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* @mat pointer to a CoglMatrix structure. The matrix inverse will be
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* stored in the CoglMatrix::inv attribute.
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*
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* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
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*
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* \author
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* Code contributed by Jacques Leroy jle@star.be
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*
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* Calculates the inverse matrix by performing the gaussian matrix reduction
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* with partial pivoting followed by back/substitution with the loops manually
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* unrolled.
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*/
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static gboolean
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invert_matrix_general (CoglMatrix *matrix)
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{
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const float *m = (float *)matrix;
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float *out = matrix->inv;
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float wtmp[4][8];
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float m0, m1, m2, m3, s;
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float *r0, *r1, *r2, *r3;
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r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
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r0[0] = MAT (m, 0, 0), r0[1] = MAT (m, 0, 1),
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r0[2] = MAT (m, 0, 2), r0[3] = MAT (m, 0, 3),
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r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
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r1[0] = MAT (m, 1, 0), r1[1] = MAT (m, 1, 1),
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r1[2] = MAT (m, 1, 2), r1[3] = MAT (m, 1, 3),
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r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
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r2[0] = MAT (m, 2, 0), r2[1] = MAT (m, 2, 1),
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r2[2] = MAT (m, 2, 2), r2[3] = MAT (m, 2, 3),
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r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
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r3[0] = MAT (m, 3, 0), r3[1] = MAT (m, 3, 1),
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r3[2] = MAT (m, 3, 2), r3[3] = MAT (m, 3, 3),
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r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
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/* choose pivot - or die */
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if (fabsf (r3[0]) > fabsf (r2[0]))
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SWAP_ROWS (r3, r2);
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if (fabsf (r2[0]) > fabsf (r1[0]))
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SWAP_ROWS (r2, r1);
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if (fabsf (r1[0]) > fabsf (r0[0]))
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SWAP_ROWS (r1, r0);
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if (0.0 == r0[0])
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return FALSE;
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/* eliminate first variable */
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m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
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s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
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s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
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s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
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s = r0[4];
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if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
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s = r0[5];
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if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
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s = r0[6];
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if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
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s = r0[7];
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if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
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/* choose pivot - or die */
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if (fabsf (r3[1]) > fabsf (r2[1]))
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SWAP_ROWS (r3, r2);
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if (fabsf (r2[1]) > fabsf (r1[1]))
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SWAP_ROWS (r2, r1);
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if (0.0 == r1[1])
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return FALSE;
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/* eliminate second variable */
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m2 = r2[1] / r1[1]; m3 = r3[1] / r1[1];
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r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
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r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
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s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
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s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
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s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
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s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
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/* choose pivot - or die */
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if (fabsf (r3[2]) > fabsf (r2[2]))
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SWAP_ROWS (r3, r2);
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if (0.0 == r2[2])
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return FALSE;
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/* eliminate third variable */
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m3 = r3[2] / r2[2];
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r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
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r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
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r3[7] -= m3 * r2[7];
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/* last check */
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if (0.0 == r3[3])
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return FALSE;
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s = 1.0f / r3[3]; /* now back substitute row 3 */
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r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
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m2 = r2[3]; /* now back substitute row 2 */
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s = 1.0f / r2[2];
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r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
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r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
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m1 = r1[3];
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r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
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r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
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m0 = r0[3];
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r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
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r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
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m1 = r1[2]; /* now back substitute row 1 */
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s = 1.0f / r1[1];
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r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
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r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
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m0 = r0[2];
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r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
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r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
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m0 = r0[1]; /* now back substitute row 0 */
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s = 1.0f / r0[0];
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r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
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r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
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MAT (out, 0, 0) = r0[4]; MAT (out, 0, 1) = r0[5],
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MAT (out, 0, 2) = r0[6]; MAT (out, 0, 3) = r0[7],
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MAT (out, 1, 0) = r1[4]; MAT (out, 1, 1) = r1[5],
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MAT (out, 1, 2) = r1[6]; MAT (out, 1, 3) = r1[7],
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MAT (out, 2, 0) = r2[4]; MAT (out, 2, 1) = r2[5],
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MAT (out, 2, 2) = r2[6]; MAT (out, 2, 3) = r2[7],
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MAT (out, 3, 0) = r3[4]; MAT (out, 3, 1) = r3[5],
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MAT (out, 3, 2) = r3[6]; MAT (out, 3, 3) = r3[7];
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return TRUE;
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}
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#undef SWAP_ROWS
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/*
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* Compute inverse of a general 3d transformation matrix.
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*
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* @mat pointer to a CoglMatrix structure. The matrix inverse will be
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* stored in the CoglMatrix::inv attribute.
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*
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* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
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*
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* \author Adapted from graphics gems II.
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*
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* Calculates the inverse of the upper left by first calculating its
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* determinant and multiplying it to the symmetric adjust matrix of each
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* element. Finally deals with the translation part by transforming the
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* original translation vector using by the calculated submatrix inverse.
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*/
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static gboolean
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invert_matrix_3d_general (CoglMatrix *matrix)
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{
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const float *in = (float *)matrix;
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float *out = matrix->inv;
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float pos, neg, t;
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float det;
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/* Calculate the determinant of upper left 3x3 submatrix and
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* determine if the matrix is singular.
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*/
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pos = neg = 0.0;
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t = MAT (in,0,0) * MAT (in,1,1) * MAT (in,2,2);
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if (t >= 0.0) pos += t; else neg += t;
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t = MAT (in,1,0) * MAT (in,2,1) * MAT (in,0,2);
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if (t >= 0.0) pos += t; else neg += t;
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t = MAT (in,2,0) * MAT (in,0,1) * MAT (in,1,2);
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if (t >= 0.0) pos += t; else neg += t;
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t = -MAT (in,2,0) * MAT (in,1,1) * MAT (in,0,2);
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if (t >= 0.0) pos += t; else neg += t;
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t = -MAT (in,1,0) * MAT (in,0,1) * MAT (in,2,2);
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if (t >= 0.0) pos += t; else neg += t;
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t = -MAT (in,0,0) * MAT (in,2,1) * MAT (in,1,2);
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if (t >= 0.0) pos += t; else neg += t;
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det = pos + neg;
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if (det*det < 1e-25)
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return FALSE;
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det = 1.0f / det;
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MAT (out,0,0) =
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( (MAT (in, 1, 1)*MAT (in, 2, 2) - MAT (in, 2, 1)*MAT (in, 1, 2) )*det);
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MAT (out,0,1) =
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(- (MAT (in, 0, 1)*MAT (in, 2, 2) - MAT (in, 2, 1)*MAT (in, 0, 2) )*det);
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MAT (out,0,2) =
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( (MAT (in, 0, 1)*MAT (in, 1, 2) - MAT (in, 1, 1)*MAT (in, 0, 2) )*det);
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MAT (out,1,0) =
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(- (MAT (in,1,0)*MAT (in,2,2) - MAT (in,2,0)*MAT (in,1,2) )*det);
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MAT (out,1,1) =
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( (MAT (in,0,0)*MAT (in,2,2) - MAT (in,2,0)*MAT (in,0,2) )*det);
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MAT (out,1,2) =
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(- (MAT (in,0,0)*MAT (in,1,2) - MAT (in,1,0)*MAT (in,0,2) )*det);
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MAT (out,2,0) =
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( (MAT (in,1,0)*MAT (in,2,1) - MAT (in,2,0)*MAT (in,1,1) )*det);
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MAT (out,2,1) =
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(- (MAT (in,0,0)*MAT (in,2,1) - MAT (in,2,0)*MAT (in,0,1) )*det);
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MAT (out,2,2) =
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( (MAT (in,0,0)*MAT (in,1,1) - MAT (in,1,0)*MAT (in,0,1) )*det);
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/* Do the translation part */
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MAT (out,0,3) = - (MAT (in, 0, 3) * MAT (out, 0, 0) +
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MAT (in, 1, 3) * MAT (out, 0, 1) +
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MAT (in, 2, 3) * MAT (out, 0, 2) );
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MAT (out,1,3) = - (MAT (in, 0, 3) * MAT (out, 1, 0) +
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MAT (in, 1, 3) * MAT (out, 1, 1) +
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MAT (in, 2, 3) * MAT (out, 1, 2) );
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MAT (out,2,3) = - (MAT (in, 0, 3) * MAT (out, 2 ,0) +
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MAT (in, 1, 3) * MAT (out, 2, 1) +
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MAT (in, 2, 3) * MAT (out, 2, 2) );
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return TRUE;
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}
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/*
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||||||
* Compute inverse of a 3d transformation matrix.
|
|
||||||
*
|
|
||||||
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
|
|
||||||
* stored in the CoglMatrix::inv attribute.
|
|
||||||
*
|
|
||||||
* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
|
|
||||||
*
|
|
||||||
* If the matrix is not an angle preserving matrix then calls
|
|
||||||
* invert_matrix_3d_general for the actual calculation. Otherwise calculates
|
|
||||||
* the inverse matrix analyzing and inverting each of the scaling, rotation and
|
|
||||||
* translation parts.
|
|
||||||
*/
|
|
||||||
static gboolean
|
|
||||||
invert_matrix_3d (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *in = (float *)matrix;
|
|
||||||
float *out = matrix->inv;
|
|
||||||
|
|
||||||
memcpy (out, identity, 16 * sizeof (float));
|
|
||||||
|
|
||||||
if (!TEST_MAT_FLAGS(matrix, MAT_FLAGS_ANGLE_PRESERVING))
|
|
||||||
return invert_matrix_3d_general (matrix);
|
|
||||||
|
|
||||||
if (matrix->flags & MAT_FLAG_UNIFORM_SCALE)
|
|
||||||
{
|
|
||||||
float scale = (MAT (in, 0, 0) * MAT (in, 0, 0) +
|
|
||||||
MAT (in, 0, 1) * MAT (in, 0, 1) +
|
|
||||||
MAT (in, 0, 2) * MAT (in, 0, 2));
|
|
||||||
|
|
||||||
if (scale == 0.0)
|
|
||||||
return FALSE;
|
|
||||||
|
|
||||||
scale = 1.0f / scale;
|
|
||||||
|
|
||||||
/* Transpose and scale the 3 by 3 upper-left submatrix. */
|
|
||||||
MAT (out, 0, 0) = scale * MAT (in, 0, 0);
|
|
||||||
MAT (out, 1, 0) = scale * MAT (in, 0, 1);
|
|
||||||
MAT (out, 2, 0) = scale * MAT (in, 0, 2);
|
|
||||||
MAT (out, 0, 1) = scale * MAT (in, 1, 0);
|
|
||||||
MAT (out, 1, 1) = scale * MAT (in, 1, 1);
|
|
||||||
MAT (out, 2, 1) = scale * MAT (in, 1, 2);
|
|
||||||
MAT (out, 0, 2) = scale * MAT (in, 2, 0);
|
|
||||||
MAT (out, 1, 2) = scale * MAT (in, 2, 1);
|
|
||||||
MAT (out, 2, 2) = scale * MAT (in, 2, 2);
|
|
||||||
}
|
|
||||||
else if (matrix->flags & MAT_FLAG_ROTATION)
|
|
||||||
{
|
|
||||||
/* Transpose the 3 by 3 upper-left submatrix. */
|
|
||||||
MAT (out, 0, 0) = MAT (in, 0, 0);
|
|
||||||
MAT (out, 1, 0) = MAT (in, 0, 1);
|
|
||||||
MAT (out, 2, 0) = MAT (in, 0, 2);
|
|
||||||
MAT (out, 0, 1) = MAT (in, 1, 0);
|
|
||||||
MAT (out, 1, 1) = MAT (in, 1, 1);
|
|
||||||
MAT (out, 2, 1) = MAT (in, 1, 2);
|
|
||||||
MAT (out, 0, 2) = MAT (in, 2, 0);
|
|
||||||
MAT (out, 1, 2) = MAT (in, 2, 1);
|
|
||||||
MAT (out, 2, 2) = MAT (in, 2, 2);
|
|
||||||
}
|
|
||||||
else
|
|
||||||
{
|
|
||||||
/* pure translation */
|
|
||||||
memcpy (out, identity, 16 * sizeof (float));
|
|
||||||
MAT (out, 0, 3) = - MAT (in, 0, 3);
|
|
||||||
MAT (out, 1, 3) = - MAT (in, 1, 3);
|
|
||||||
MAT (out, 2, 3) = - MAT (in, 2, 3);
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
|
|
||||||
if (matrix->flags & MAT_FLAG_TRANSLATION)
|
|
||||||
{
|
|
||||||
/* Do the translation part */
|
|
||||||
MAT (out,0,3) = - (MAT (in, 0, 3) * MAT (out, 0, 0) +
|
|
||||||
MAT (in, 1, 3) * MAT (out, 0, 1) +
|
|
||||||
MAT (in, 2, 3) * MAT (out, 0, 2) );
|
|
||||||
MAT (out,1,3) = - (MAT (in, 0, 3) * MAT (out, 1, 0) +
|
|
||||||
MAT (in, 1, 3) * MAT (out, 1, 1) +
|
|
||||||
MAT (in, 2, 3) * MAT (out, 1, 2) );
|
|
||||||
MAT (out,2,3) = - (MAT (in, 0, 3) * MAT (out, 2, 0) +
|
|
||||||
MAT (in, 1, 3) * MAT (out, 2, 1) +
|
|
||||||
MAT (in, 2, 3) * MAT (out, 2, 2) );
|
|
||||||
}
|
|
||||||
else
|
|
||||||
MAT (out, 0, 3) = MAT (out, 1, 3) = MAT (out, 2, 3) = 0.0;
|
|
||||||
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Compute inverse of an identity transformation matrix.
|
|
||||||
*
|
|
||||||
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
|
|
||||||
* stored in the CoglMatrix::inv attribute.
|
|
||||||
*
|
|
||||||
* Returns: always %TRUE.
|
|
||||||
*
|
|
||||||
* Simply copies identity into CoglMatrix::inv.
|
|
||||||
*/
|
|
||||||
static gboolean
|
|
||||||
invert_matrix_identity (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
memcpy (matrix->inv, identity, 16 * sizeof (float));
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Compute inverse of a no-rotation 3d transformation matrix.
|
|
||||||
*
|
|
||||||
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
|
|
||||||
* stored in the CoglMatrix::inv attribute.
|
|
||||||
*
|
|
||||||
* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
|
|
||||||
*
|
|
||||||
* Calculates the
|
|
||||||
*/
|
|
||||||
static gboolean
|
|
||||||
invert_matrix_3d_no_rotation (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *in = (float *)matrix;
|
|
||||||
float *out = matrix->inv;
|
|
||||||
|
|
||||||
if (MAT (in,0,0) == 0 || MAT (in,1,1) == 0 || MAT (in,2,2) == 0)
|
|
||||||
return FALSE;
|
|
||||||
|
|
||||||
memcpy (out, identity, 16 * sizeof (float));
|
|
||||||
MAT (out,0,0) = 1.0f / MAT (in,0,0);
|
|
||||||
MAT (out,1,1) = 1.0f / MAT (in,1,1);
|
|
||||||
MAT (out,2,2) = 1.0f / MAT (in,2,2);
|
|
||||||
|
|
||||||
if (matrix->flags & MAT_FLAG_TRANSLATION)
|
|
||||||
{
|
|
||||||
MAT (out,0,3) = - (MAT (in,0,3) * MAT (out,0,0));
|
|
||||||
MAT (out,1,3) = - (MAT (in,1,3) * MAT (out,1,1));
|
|
||||||
MAT (out,2,3) = - (MAT (in,2,3) * MAT (out,2,2));
|
|
||||||
}
|
|
||||||
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Compute inverse of a no-rotation 2d transformation matrix.
|
|
||||||
*
|
|
||||||
* @mat pointer to a CoglMatrix structure. The matrix inverse will be
|
|
||||||
* stored in the CoglMatrix::inv attribute.
|
|
||||||
*
|
|
||||||
* Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
|
|
||||||
*
|
|
||||||
* Calculates the inverse matrix by applying the inverse scaling and
|
|
||||||
* translation to the identity matrix.
|
|
||||||
*/
|
|
||||||
static gboolean
|
|
||||||
invert_matrix_2d_no_rotation (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *in = (float *)matrix;
|
|
||||||
float *out = matrix->inv;
|
|
||||||
|
|
||||||
if (MAT (in, 0, 0) == 0 || MAT (in, 1, 1) == 0)
|
|
||||||
return FALSE;
|
|
||||||
|
|
||||||
memcpy (out, identity, 16 * sizeof (float));
|
|
||||||
MAT (out, 0, 0) = 1.0f / MAT (in, 0, 0);
|
|
||||||
MAT (out, 1, 1) = 1.0f / MAT (in, 1, 1);
|
|
||||||
|
|
||||||
if (matrix->flags & MAT_FLAG_TRANSLATION)
|
|
||||||
{
|
|
||||||
MAT (out, 0, 3) = - (MAT (in, 0, 3) * MAT (out, 0, 0));
|
|
||||||
MAT (out, 1, 3) = - (MAT (in, 1, 3) * MAT (out, 1, 1));
|
|
||||||
}
|
|
||||||
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
|
|
||||||
#if 0
|
|
||||||
/* broken */
|
|
||||||
static gboolean
|
|
||||||
invert_matrix_perspective (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *in = matrix;
|
|
||||||
float *out = matrix->inv;
|
|
||||||
|
|
||||||
if (MAT (in,2,3) == 0)
|
|
||||||
return FALSE;
|
|
||||||
|
|
||||||
memcpy( out, identity, 16 * sizeof(float) );
|
|
||||||
|
|
||||||
MAT (out, 0, 0) = 1.0f / MAT (in, 0, 0);
|
|
||||||
MAT (out, 1, 1) = 1.0f / MAT (in, 1, 1);
|
|
||||||
|
|
||||||
MAT (out, 0, 3) = MAT (in, 0, 2);
|
|
||||||
MAT (out, 1, 3) = MAT (in, 1, 2);
|
|
||||||
|
|
||||||
MAT (out,2,2) = 0;
|
|
||||||
MAT (out,2,3) = -1;
|
|
||||||
|
|
||||||
MAT (out,3,2) = 1.0f / MAT (in,2,3);
|
|
||||||
MAT (out,3,3) = MAT (in,2,2) * MAT (out,3,2);
|
|
||||||
|
|
||||||
return TRUE;
|
|
||||||
}
|
|
||||||
#endif
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Matrix inversion function pointer type.
|
|
||||||
*/
|
|
||||||
typedef gboolean (*inv_mat_func)(CoglMatrix *matrix);
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Table of the matrix inversion functions according to the matrix type.
|
|
||||||
*/
|
|
||||||
static inv_mat_func inv_mat_tab[7] = {
|
|
||||||
invert_matrix_general,
|
|
||||||
invert_matrix_identity,
|
|
||||||
invert_matrix_3d_no_rotation,
|
|
||||||
#if 0
|
|
||||||
/* Don't use this function for now - it fails when the projection matrix
|
|
||||||
* is premultiplied by a translation (ala Chromium's tilesort SPU).
|
|
||||||
*/
|
|
||||||
invert_matrix_perspective,
|
|
||||||
#else
|
|
||||||
invert_matrix_general,
|
|
||||||
#endif
|
|
||||||
invert_matrix_3d, /* lazy! */
|
|
||||||
invert_matrix_2d_no_rotation,
|
|
||||||
invert_matrix_3d
|
|
||||||
};
|
|
||||||
|
|
||||||
#define ZERO(x) (1<<x)
|
|
||||||
#define ONE(x) (1<<(x+16))
|
|
||||||
|
|
||||||
#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
|
|
||||||
#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
|
|
||||||
|
|
||||||
#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
|
|
||||||
ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
|
|
||||||
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
|
|
||||||
|
|
||||||
#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
|
|
||||||
ZERO(1) | ZERO(9) | \
|
|
||||||
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
|
|
||||||
|
|
||||||
#define MASK_2D ( ZERO(8) | \
|
|
||||||
ZERO(9) | \
|
|
||||||
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
|
|
||||||
|
|
||||||
|
|
||||||
#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
|
|
||||||
ZERO(1) | ZERO(9) | \
|
|
||||||
ZERO(2) | ZERO(6) | \
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
|
|
||||||
|
|
||||||
#define MASK_3D ( \
|
|
||||||
\
|
|
||||||
\
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
|
|
||||||
|
|
||||||
|
|
||||||
#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
|
|
||||||
ZERO(1) | ZERO(13) |\
|
|
||||||
ZERO(2) | ZERO(6) | \
|
|
||||||
ZERO(3) | ZERO(7) | ZERO(15) )
|
|
||||||
|
|
||||||
#define SQ(x) ((x)*(x))
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Determine type and flags from scratch.
|
|
||||||
*
|
|
||||||
* This is expensive enough to only want to do it once.
|
|
||||||
*/
|
|
||||||
static void
|
|
||||||
analyse_from_scratch (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *m = (float *)matrix;
|
|
||||||
unsigned int mask = 0;
|
|
||||||
unsigned int i;
|
|
||||||
|
|
||||||
for (i = 0 ; i < 16 ; i++)
|
|
||||||
{
|
|
||||||
if (m[i] == 0.0) mask |= (1<<i);
|
|
||||||
}
|
|
||||||
|
|
||||||
if (m[0] == 1.0f) mask |= (1<<16);
|
|
||||||
if (m[5] == 1.0f) mask |= (1<<21);
|
|
||||||
if (m[10] == 1.0f) mask |= (1<<26);
|
|
||||||
if (m[15] == 1.0f) mask |= (1<<31);
|
|
||||||
|
|
||||||
matrix->flags &= ~MAT_FLAGS_GEOMETRY;
|
|
||||||
|
|
||||||
/* Check for translation - no-one really cares
|
|
||||||
*/
|
|
||||||
if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
|
|
||||||
matrix->flags |= MAT_FLAG_TRANSLATION;
|
|
||||||
|
|
||||||
/* Do the real work
|
|
||||||
*/
|
|
||||||
if (mask == (unsigned int) MASK_IDENTITY)
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_IDENTITY;
|
|
||||||
else if ((mask & MASK_2D_NO_ROT) == (unsigned int) MASK_2D_NO_ROT)
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
|
|
||||||
|
|
||||||
if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
|
|
||||||
}
|
|
||||||
else if ((mask & MASK_2D) == (unsigned int) MASK_2D)
|
|
||||||
{
|
|
||||||
float mm = DOT2 (m, m);
|
|
||||||
float m4m4 = DOT2 (m+4,m+4);
|
|
||||||
float mm4 = DOT2 (m,m+4);
|
|
||||||
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_2D;
|
|
||||||
|
|
||||||
/* Check for scale */
|
|
||||||
if (SQ (mm-1) > SQ (1e-6) ||
|
|
||||||
SQ (m4m4-1) > SQ (1e-6))
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
|
|
||||||
|
|
||||||
/* Check for rotation */
|
|
||||||
if (SQ (mm4) > SQ (1e-6))
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_3D;
|
|
||||||
else
|
|
||||||
matrix->flags |= MAT_FLAG_ROTATION;
|
|
||||||
|
|
||||||
}
|
|
||||||
else if ((mask & MASK_3D_NO_ROT) == (unsigned int) MASK_3D_NO_ROT)
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
|
|
||||||
|
|
||||||
/* Check for scale */
|
|
||||||
if (SQ (m[0]-m[5]) < SQ (1e-6) &&
|
|
||||||
SQ (m[0]-m[10]) < SQ (1e-6))
|
|
||||||
{
|
|
||||||
if (SQ (m[0]-1.0) > SQ (1e-6))
|
|
||||||
matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
|
|
||||||
}
|
|
||||||
else if ((mask & MASK_3D) == (unsigned int) MASK_3D)
|
|
||||||
{
|
|
||||||
float c1 = DOT3 (m,m);
|
|
||||||
float c2 = DOT3 (m+4,m+4);
|
|
||||||
float c3 = DOT3 (m+8,m+8);
|
|
||||||
float d1 = DOT3 (m, m+4);
|
|
||||||
float cp[3];
|
|
||||||
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_3D;
|
|
||||||
|
|
||||||
/* Check for scale */
|
|
||||||
if (SQ (c1-c2) < SQ (1e-6) && SQ (c1-c3) < SQ (1e-6))
|
|
||||||
{
|
|
||||||
if (SQ (c1-1.0) > SQ (1e-6))
|
|
||||||
matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
|
|
||||||
/* else no scale at all */
|
|
||||||
}
|
|
||||||
else
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_SCALE;
|
|
||||||
|
|
||||||
/* Check for rotation */
|
|
||||||
if (SQ (d1) < SQ (1e-6))
|
|
||||||
{
|
|
||||||
CROSS3 ( cp, m, m+4);
|
|
||||||
SUB_3V ( cp, cp, (m+8));
|
|
||||||
if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
|
|
||||||
matrix->flags |= MAT_FLAG_ROTATION;
|
|
||||||
else
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_3D;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
|
|
||||||
}
|
|
||||||
else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0f)
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_GENERAL;
|
|
||||||
matrix->flags |= MAT_FLAG_GENERAL;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Analyze a matrix given that its flags are accurate.
|
|
||||||
*
|
|
||||||
* This is the more common operation, hopefully.
|
|
||||||
*/
|
|
||||||
static void
|
|
||||||
analyse_from_flags (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
const float *m = (float *)matrix;
|
|
||||||
|
|
||||||
if (TEST_MAT_FLAGS(matrix, 0))
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_IDENTITY;
|
|
||||||
else if (TEST_MAT_FLAGS(matrix, (MAT_FLAG_TRANSLATION |
|
|
||||||
MAT_FLAG_UNIFORM_SCALE |
|
|
||||||
MAT_FLAG_GENERAL_SCALE)))
|
|
||||||
{
|
|
||||||
if ( m[10] == 1.0f && m[14] == 0.0f )
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
|
|
||||||
else
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
|
|
||||||
}
|
|
||||||
else if (TEST_MAT_FLAGS (matrix, MAT_FLAGS_3D))
|
|
||||||
{
|
|
||||||
if ( m[ 8]==0.0f
|
|
||||||
&& m[ 9]==0.0f
|
|
||||||
&& m[2]==0.0f && m[6]==0.0f && m[10]==1.0f && m[14]==0.0f)
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_2D;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_3D;
|
|
||||||
}
|
|
||||||
else if ( m[4]==0.0f && m[12]==0.0f
|
|
||||||
&& m[1]==0.0f && m[13]==0.0f
|
|
||||||
&& m[2]==0.0f && m[6]==0.0f
|
|
||||||
&& m[3]==0.0f && m[7]==0.0f && m[11]==-1.0f && m[15]==0.0f)
|
|
||||||
{
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
matrix->type = COGL_MATRIX_TYPE_GENERAL;
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Analyze and update the type and flags of a matrix.
|
|
||||||
*
|
|
||||||
* If the matrix type is dirty then calls either analyse_from_scratch() or
|
|
||||||
* analyse_from_flags() to determine its type, according to whether the flags
|
|
||||||
* are dirty or not, respectively. If the matrix has an inverse and it's dirty
|
|
||||||
* then calls matrix_invert(). Finally clears the dirty flags.
|
|
||||||
*/
|
|
||||||
static void
|
|
||||||
_cogl_matrix_update_type_and_flags (CoglMatrix *matrix)
|
|
||||||
{
|
|
||||||
if (matrix->flags & MAT_DIRTY_TYPE)
|
|
||||||
{
|
|
||||||
if (matrix->flags & MAT_DIRTY_FLAGS)
|
|
||||||
analyse_from_scratch (matrix);
|
|
||||||
else
|
|
||||||
analyse_from_flags (matrix);
|
|
||||||
}
|
|
||||||
|
|
||||||
matrix->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
/*
|
||||||
* Compute inverse of a transformation matrix.
|
* Compute inverse of a transformation matrix.
|
||||||
*
|
*
|
||||||
@ -1029,23 +327,58 @@ _cogl_matrix_update_type_and_flags (CoglMatrix *matrix)
|
|||||||
* given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
|
* given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
|
||||||
* and copies the identity matrix into CoglMatrix::inv.
|
* and copies the identity matrix into CoglMatrix::inv.
|
||||||
*/
|
*/
|
||||||
|
|
||||||
|
static inline gboolean
|
||||||
|
calculate_inverse (CoglMatrix *matrix)
|
||||||
|
{
|
||||||
|
graphene_matrix_t inverse;
|
||||||
|
graphene_matrix_t scaled;
|
||||||
|
graphene_matrix_t m;
|
||||||
|
gboolean invertible;
|
||||||
|
float pivot = G_MAXFLOAT;
|
||||||
|
float v[16];
|
||||||
|
float scale;
|
||||||
|
|
||||||
|
cogl_matrix_to_graphene_matrix (matrix, &m);
|
||||||
|
graphene_matrix_to_float (&m, v);
|
||||||
|
|
||||||
|
pivot = MIN (pivot, v[0]);
|
||||||
|
pivot = MIN (pivot, v[5]);
|
||||||
|
pivot = MIN (pivot, v[10]);
|
||||||
|
pivot = MIN (pivot, v[15]);
|
||||||
|
scale = 1.f / pivot;
|
||||||
|
|
||||||
|
graphene_matrix_init_scale (&scaled, scale, scale, scale);
|
||||||
|
|
||||||
|
/* Float precision is a limiting factor */
|
||||||
|
graphene_matrix_multiply (&m, &scaled, &m);
|
||||||
|
|
||||||
|
invertible = graphene_matrix_inverse (&m, &inverse);
|
||||||
|
|
||||||
|
if (invertible)
|
||||||
|
graphene_matrix_multiply (&scaled, &inverse, &inverse);
|
||||||
|
else
|
||||||
|
graphene_matrix_init_identity (&inverse);
|
||||||
|
|
||||||
|
graphene_matrix_to_float (&inverse, matrix->inv);
|
||||||
|
|
||||||
|
return invertible;
|
||||||
|
}
|
||||||
|
|
||||||
static gboolean
|
static gboolean
|
||||||
_cogl_matrix_update_inverse (CoglMatrix *matrix)
|
_cogl_matrix_update_inverse (CoglMatrix *matrix)
|
||||||
{
|
{
|
||||||
if (matrix->flags & MAT_DIRTY_FLAGS ||
|
if (matrix->flags & MAT_DIRTY_FLAGS ||
|
||||||
matrix->flags & MAT_DIRTY_INVERSE)
|
matrix->flags & MAT_DIRTY_INVERSE)
|
||||||
{
|
{
|
||||||
_cogl_matrix_update_type_and_flags (matrix);
|
if (calculate_inverse (matrix))
|
||||||
|
|
||||||
if (inv_mat_tab[matrix->type](matrix))
|
|
||||||
matrix->flags &= ~MAT_FLAG_SINGULAR;
|
matrix->flags &= ~MAT_FLAG_SINGULAR;
|
||||||
else
|
else
|
||||||
{
|
|
||||||
matrix->flags |= MAT_FLAG_SINGULAR;
|
matrix->flags |= MAT_FLAG_SINGULAR;
|
||||||
memcpy (matrix->inv, identity, 16 * sizeof (float));
|
|
||||||
}
|
|
||||||
|
|
||||||
matrix->flags &= ~MAT_DIRTY_INVERSE;
|
matrix->flags &= ~(MAT_DIRTY_FLAGS |
|
||||||
|
MAT_DIRTY_TYPE |
|
||||||
|
MAT_DIRTY_INVERSE);
|
||||||
}
|
}
|
||||||
|
|
||||||
if (matrix->flags & MAT_FLAG_SINGULAR)
|
if (matrix->flags & MAT_FLAG_SINGULAR)
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user