README.md: mention also the tetraflexagon example

[flexagon-toolkit.git] / src / diagram / diagram.py

diff --git a/src/diagram/diagram.py b/src/diagram/diagram.py
index 43e3a93..e6c51c4 100755 (executable)
--- a/src/diagram/diagram.py
+++ b/src/diagram/diagram.py
@@ -127,6 +127,66 @@ class Diagram(object):
         return fmod(theta, 2 * pi) / (2 * pi)
 
     @staticmethod
+    def calc_rotate_translate_transform(src_x, src_y, dest_x, dest_y, theta):
+        """Calculate the transformation matrix resulting from a rotation and
+        a translation.
+
+        Return the matrix as a list of values sorted in row-major order."""
+
+        # A rotate-translate transformation is composed by these steps:
+        #
+        #   1. rotate by 'theta' around (src_x, src_y);
+        #   2. move to (dest_x, dest_y).
+        #
+        # Step 1 can be expressed by these sub-steps:
+        #
+        #  1a. translate by (-src_x, -src_y)
+        #  1b. rotate by 'theta'
+        #  1c. translate by (src_x, src_y)
+        #
+        # Step 2. can be expressed by a translation like:
+        #
+        #  2a. translate by (dest_x - src_x, dest_y - src_y)
+        #
+        # The consecutive translations 1c and 2a can be easily combined, so
+        # the final steps are:
+        #
+        #  T1 -> translate by (-src_x, -src_y)
+        #  R  -> rotate by 'theta'
+        #  T2 -> translate by (dest_x, dest_y)
+        #
+        # Using affine transformations these are expressed as:
+        #
+        #      | 1  0  -src_x |
+        # T1 = | 0  1  -src_y |
+        #      | 0  0       1 |
+        #
+        #      | cos(theta)  -sin(theta)  0 |
+        # R  = | sin(theta)   cos(theta)  0 |
+        #      |          0            0  1 |
+        #
+        #      | 1  0  dest_x |
+        # T2 = | 0  1  dest_y |
+        #      | 0  0       1 |
+        #
+        # Composing these transformations into one is achieved by multiplying
+        # the matrices from right to left:
+        #
+        #   T = T2 * R * T1
+        #
+        # NOTE: To remember this think about composing functions: T2(R(T1())),
+        # the inner one is performed first.
+        #
+        # The resulting  T matrix is the one below.
+        matrix = [
+            cos(theta), -sin(theta), -src_x * cos(theta) + src_y * sin(theta) + dest_x,
+            sin(theta),  cos(theta), -src_x * sin(theta) - src_y * cos(theta) + dest_y,
+                     0,           0,                                                 1
+        ]
+
+        return matrix
+
+    @staticmethod
     def get_regular_polygon(x, y, sides, r, theta0=0.0):
         """Calc the coordinates of the regular polygon.