5 files changed, 137 insertions, 10 deletions

diff --git a/include/common/geom.h b/include/common/geom.h
index b3564a5..334e95c 100644
--- a/include/common/geom.h
+++ b/include/common/geom.h
@@ -15,6 +15,12 @@
 typedef int32_t IntVector;
 
 /**
+ * Type: RealVector
+ * An abstract 1-D real vector.
+ */
+typedef double RealVector;
+
+/**
  * Struct: CartesianVector
  * An abstract 2-D vector in cartesian coordinates.
  *
@@ -27,6 +33,19 @@ typedef struct {
 } CartesianVector;
 
 /**
+ * Struct: BarycentricVector
+ * An abstract barycentric coordinate tuple relative to a triangle.
+ * The third barycentric coordinate is deduced from the first two ones.
+ *
+ * Fields:
+ *   a - the first barycentric coordinate
+ *   b - the second barycentric coordinate
+ */
+typedef struct {
+  RealVector a, b;
+} BarycentricVector;
+
+/**
  * Struct: CartesianMapping
  * A tuple of cartesian vectors representing a mapping.
  *
@@ -38,6 +57,16 @@ typedef struct {
   CartesianVector origin, target;
 } CartesianMapping;
 
+/**
+ * Struct: Triangle
+ * Represents a simple triangle with three vertices.
+ *
+ * Fields:
+ *   v[] - array of vertices
+ */
+typedef struct {
+  CartesianVector v[3];
+} Triangle;
 
 /**
  * Function: m
@@ -66,6 +95,19 @@ CartesianMapping m(int x, int y);
 CartesianVector v(int x, int y);
 
 /**
+ * Function: b
+ * Shorthand for a barycentric vector.
+ *
+ * Parameters:
+ *   a - the a-coordinate
+ *   b - the b-coordinate
+ *
+ * Returns:
+ *   A barycentric vector
+ */
+BarycentricVector b(double a, double b);
+
+/**
  * Function: mappings_equals
  * Compares two cartesian mappings.
  *
@@ -92,17 +134,54 @@ bool mappings_equals(CartesianMapping m1, CartesianMapping m2);
 bool vector_equals(CartesianVector v1, CartesianVector v2);
 
 /**
- * Function: triangle_area
- * Computes the area of a triangle.
+ * Function: barycentric_vector_equals
+ * Compares two barycentric vectors.
+ *
+ * Parameters:
+ *   v1 - the first vector
+ *   v2 - the second vector
+ *
+ * Returns:
+ *   T(v1 is equal to v2)
+ */
+bool barycentric_vector_equals(BarycentricVector b1, BarycentricVector b2);
+
+/**
+ * Function: square_area
+ * Computes the area of a square spawned by three positively oriented vertices.
+ *
+ * Parameters:
+ *   vi - vertices
+ *
+ * Returns:
+ *   The area of the square
+ */
+IntVector square_area(CartesianVector v1, CartesianVector v2, CartesianVector v3);
+
+/**
+ * Function: cartesian_to_barycentric
+ * Computes and returns the barycentric coordinates of a given point in the given reference triangle.
+ *
+ * Parameters:
+ *   t - reference triangle
+ *   p - the vector to convert
+ *
+ * Returns:
+ *   The barycentric coordinates vector
+ */
+BarycentricVector cartesian_to_barycentric(Triangle t, CartesianVector p);
+
+/**
+ * Function: barycentric_to_cartesian
+ * Computes and returns the cartesian coordinates of a given point in the given reference triangle.
  *
  * Parameters:
- *   v1 - first vertex
- *   v2 - second vertex
- *   v3 - third vertex
+ *   t - reference triangle
+ *   p - the vector to convert
  *
  * Returns:
- *   The area of the triangle spawned by the three supplied vertices
+ *   The cartesian coordinate vector
  */
-IntVector triangle_area(CartesianVector v1, CartesianVector v2, CartesianVector v3);
+CartesianVector barycentric_to_cartesian(Triangle t, BarycentricVector p);
 
 #endif
diff --git a/include/common/time.h b/include/common/time.h
index 54a7bb2..e207ad7 100644
--- a/include/common/time.h
+++ b/include/common/time.h
@@ -5,6 +5,8 @@
  * File: time.h
  */
 
+#include "geom.h"
+
 /**
  * Constants: Time vectors
  *
@@ -18,6 +20,6 @@
  * Type: TimeVector
  * An abstract time vector.
  */
-typedef float TimeVector;
+typedef RealVector TimeVector;
 
 #endif
diff --git a/src/common/geom.c b/src/common/geom.c
index 219270f..eb35727 100644
--- a/src/common/geom.c
+++ b/src/common/geom.c
@@ -1,6 +1,12 @@
 #include "common/geom.h"
+#include <math.h>
+#include <common/geom.h>
 #include "morpher/matrix.h"
 
+static inline IntVector int_round(RealVector x) {
+  return (IntVector) round(x);
+}
+
 CartesianMapping m(int x, int y) {
   return (CartesianMapping) {{x, y},
                              {x, y}};
@@ -10,6 +16,10 @@ CartesianVector v(int x, int y) {
   return (CartesianVector) {x, y};
 }
 
+BarycentricVector b(double a, double b) {
+  return (BarycentricVector) {a, b};
+}
+
 bool mappings_equals(CartesianMapping m1, CartesianMapping m2) {
   return vector_equals(m1.origin, m2.origin) && vector_equals(m1.target, m2.target);
 }
@@ -18,7 +28,22 @@ 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) {
+bool barycentric_vector_equals(BarycentricVector b1, BarycentricVector b2) {
+  return b1.a == b2.a && b1.b == b2.b;
+}
+
+IntVector square_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);
 }
+
+BarycentricVector cartesian_to_barycentric(Triangle t, CartesianVector p) {
+  RealVector total_area = square_area(t.v[0], t.v[1], t.v[2]);
+  return (BarycentricVector) {square_area(t.v[1], t.v[2], p) / total_area,
+                              square_area(t.v[2], t.v[0], p) / total_area};
+}
+
+CartesianVector barycentric_to_cartesian(Triangle t, BarycentricVector p) {
+  return (CartesianVector) {int_round(p.a * (t.v[0].x - t.v[2].x) + p.b * (t.v[1].x - t.v[2].x) + t.v[2].x),
+                            int_round(p.a * (t.v[0].y - t.v[2].y) + p.b * (t.v[1].y - t.v[2].y) + t.v[2].y)};
+}
diff --git a/src/morpher/trianglemap.c b/src/morpher/trianglemap.c
index e2f3eb9..ad526bc 100644
--- a/src/morpher/trianglemap.c
+++ b/src/morpher/trianglemap.c
@@ -30,7 +30,7 @@ TriangleMap *trianglemap_to(TriangleMap *t, CartesianVector v) {
   int edge;
 
   for (edge = 0; edge < 3; ++edge)
-    if (triangle_area(t->vertices[edge].origin, t->vertices[(edge + 1) % 3].origin, v) > 0)
+    if (square_area(t->vertices[edge].origin, t->vertices[(edge + 1) % 3].origin, v) > 0)
       return t->neighbors[edge];
 
   return t;
diff --git a/test/common/geom.c b/test/common/geom.c
new file mode 100644
index 0000000..f05e0a1
--- /dev/null
+++ b/test/common/geom.c
@@ -0,0 +1,21 @@
+#include "common/geom.h"
+#include <assert.h>
+
+static void test_square_area() {
+  assert(square_area(v(0, 0), v(10, 0), v(10, 10)) == 100);
+  assert(square_area(v(0, 0), v(0, 10), v(10, 10)) == -100);
+}
+
+static void test_cartesian_barycentric_vectors() {
+  Triangle t = {{v(0, 0), v(10, 0), v(10, 10)}};
+  CartesianVector c = v(3, 2);