Simplify and add geom. and matrix utility functions

Signed-off-by: pacien <pacien.trangirard@pacien.net>

8 files changed, 149 insertions, 135 deletions

diff --git a/include/common/geom.h b/include/common/geom.h
index a843c76..b3564a5 100644
--- a/include/common/geom.h
+++ b/include/common/geom.h
@@ -38,6 +38,46 @@ typedef struct {
   CartesianVector origin, target;
 } CartesianMapping;
 
+
+/**
+ * Function: m
+ * Shorthand for an identity mapping.
+ *
+ * Parameters:
+ *   x - the x-coordinate
+ *   y - the y-coordinate
+ *
+ * Returns:
+ *   A cartesian identity mapping
+ */
+CartesianMapping m(int x, int y);
+
+/**
+ * Function: v
+ * Shorthand for a vector.
+ *
+ * Parameters:
+ *   x - the x-coordinate
+ *   y - the y-coordinate
+ *
+ * Returns:
+ *   An integer vector
+ */
+CartesianVector v(int x, int y);
+
+/**
+ * Function: mappings_equals
+ * Compares two cartesian mappings.
+ *
+ * Parameters:
+ *   m1 - the first mapping
+ *   m2 - the second mapping
+ *
+ * Returns:
+ *   T(m1 is equal to m2)
+ */
+bool mappings_equals(CartesianMapping m1, CartesianMapping m2);
+
 /**
  * Function: vector_equals
  * Compares two cartesian vectors.
@@ -51,4 +91,18 @@ typedef struct {
  */
 bool vector_equals(CartesianVector v1, CartesianVector v2);
 
+/**
+ * Function: triangle_area
+ * Computes the area of a triangle.
+ *
+ * Parameters:
+ *   v1 - first vertex
+ *   v2 - second vertex
+ *   v3 - third vertex
+ *
+ * Returns:
+ *   The area of the triangle spawned by the three supplied vertices
+ */
+IntVector triangle_area(CartesianVector v1, CartesianVector v2, CartesianVector v3);
+
 #endif
diff --git a/include/common/matrix.h b/include/common/matrix.h
deleted file mode 100644
index fe4a12a..0000000
--- a/include/common/matrix.h
+++ /dev/null
@@ -1,51 +0,0 @@
-#ifndef UPEM_MORPHING_MATRIX
-#define UPEM_MORPHING_MATRIX
-
-/**
- * File: matrix.h
- * Matrices representation and useful operations.
- *
- * See also:
- *   The film
- */
-
-#include "geom.h"
-
-/**
- * Struct: IntSquareMatrix
- * Represents a square integer matrix.
- *
- * Fields:
- *   **elements - NULL-terminated array of element pointers
- *   dim        - dimension
- */
-typedef struct {
-  IntVector **elements;
-  IntVector dim;
-} IntSquareMatrix;
-
-/**
- * Function: matrix_int_det
- * Computes and returns the determinant of a square integer matrix.
- *
- * Parameters:
- *   *matrix - pointer to input matrix
- *
- * Returns:
- *   The integer determinant
- */
-IntVector matrix_int_det(IntSquareMatrix *matrix);
-
-/**
- * Function: matrix_reshape
- * Reshapes a flat vector into a bi-dimensional row pointer array.
- *
- * Parameters:
- *   **bi_dim - pointer to the result row array
- *   *flat    - flat vector
- *   width    - number of elements per row
- *   height   - number of rows
- */
-void matrix_reshape(IntVector **bi_dim, IntVector *flat, int width, int height);
-
-#endif
diff --git a/include/morpher/matrix.h b/include/morpher/matrix.h
new file mode 100644
index 0000000..8118727
--- /dev/null
+++ b/include/morpher/matrix.h
@@ -0,0 +1,41 @@
+#ifndef UPEM_MORPHING_MATRIX
+#define UPEM_MORPHING_MATRIX
+
+/**
+ * File: matrix.h
+ * Determinant operations.
+ *
+ * See also:
+ *   The film
+ */
+
+#include "common/geom.h"
+
+/**
+ * Function: matrix_int_det2
+ * Computes and returns the determinant of a square integer matrix of size 2.
+ *
+ * Parameters:
+ *   uij - element at the i-th row and j-th column, counting from 1
+ *
+ * Returns:
+ *   The integer determinant
+ */
+IntVector matrix_int_det2(IntVector u11, IntVector u12,
+                          IntVector u21, IntVector u22);
+
+/**
+ * Function: matrix_int_det3
+ * Computes and returns the determinant of a square integer matrix of size 3.
+ *
+ * Parameters:
+ *   uij - element at the i-th row and j-th column, counting from 1
+ *
+ * Returns:
+ *   The integer determinant
+ */
+IntVector matrix_int_det3(IntVector u11, IntVector u12, IntVector u13,
+                          IntVector u21, IntVector u22, IntVector u23,
+                          IntVector u31, IntVector u32, IntVector u33);
+
+#endif
diff --git a/src/common/geom.c b/src/common/geom.c
index 7abb422..219270f 100644
--- a/src/common/geom.c
+++ b/src/common/geom.c
@@ -1,5 +1,24 @@
 #include "common/geom.h"
+#include "morpher/matrix.h"
+
+CartesianMapping m(int x, int y) {
+  return (CartesianMapping) {{x, y},
+                             {x, y}};
+}
+
+CartesianVector v(int x, int y) {
+  return (CartesianVector) {x, y};
+}
+
+bool mappings_equals(CartesianMapping m1, CartesianMapping m2) {
+  return vector_equals(m1.origin, m2.origin) && vector_equals(m1.target, m2.target);
+}
 
 bool vector_equals(CartesianVector v1, CartesianVector v2) {
   return v1.x == v2.x && v1.y == v2.y;
 }
+
+IntVector triangle_area(CartesianVector v1, CartesianVector v2, CartesianVector v3) {
+  return matrix_int_det2(v1.x - v3.x, v2.x - v3.x,
+                         v1.y - v3.y, v2.y - v3.y);
+}
diff --git a/src/common/matrix.c b/src/common/matrix.c
deleted file mode 100644
index 60f9afb..0000000
--- a/src/common/matrix.c
+++ /dev/null
@@ -1,63 +0,0 @@
-#include "common/matrix.h"
-#include <assert.h>
-#include <memory.h>
-#include <stdlib.h>
-#include "common/mem.h"
-
-static inline IntSquareMatrix *matrix_without_row(IntSquareMatrix *target, IntSquareMatrix *origin,
-                                                  IntVector omitted_row) {
-  int origin_row, target_row;
-
-  for (origin_row = 0, target_row = 0; origin_row < origin->dim; ++origin_row)
-    if (origin_row != omitted_row)
-      target->elements[target_row++] = origin->elements[origin_row];
-
-  return target;
-}
-
-static inline IntVector det_dev_sign(IntVector row, IntVector col) {
-  assert(row > 0 && col > 0);
-  return ((row + col) % 2 == 0) ? 1 : -1;
-}
-
-static inline IntVector det_reduce(IntSquareMatrix *matrix) {
-  IntSquareMatrix sub_matrix;
-  int row;
-  IntVector det = 0;
-
-  assert(matrix->dim > 2);
-
-  sub_matrix.dim = matrix->dim - 1;
-  sub_matrix.elements = malloc_or_die(sub_matrix.dim * sizeof(IntVector *));
-
-  for (row = 0; row < matrix->dim; ++row)
-    det += matrix->elements[row][matrix->dim - 1]
-           * det_dev_sign(row + 1, matrix->dim)
-           * matrix_int_det(matrix_without_row(&sub_matrix, matrix, row));
-
-
-  free(sub_matrix.elements);
-  return det;
-}
-
-IntVector matrix_int_det(IntSquareMatrix *matrix) {
-  assert(matrix->dim > 0);
-  switch (matrix->dim) {
-    case 1:
-      return matrix->elements[0][0];
-
-    case 2:
-      return matrix->elements[0][0] * matrix->elements[1][1] - matrix->elements[0][1] * matrix->elements[1][0];