Implement drawing a Pascal triangle

This uses very basic graphics and is not yet interactive.

1 files changed, 59 insertions, 1 deletions

diff --git a/PascalTriangle.activity/pascaltriangle.py b/PascalTriangle.activity/pascaltriangle.py
index 825fc9f..2acd364 100755
--- a/PascalTriangle.activity/pascaltriangle.py
+++ b/PascalTriangle.activity/pascaltriangle.py
@@ -26,10 +26,68 @@ class PascalTriangleActivity(activity.Activity):
         # The final step is to display this newly created widget.
         self.drawing_area.show()
 
+        # Set the initial size of the Pascal triangle to be drawn. This is
+        # the number of cells on its base (equivalently, the number of rows in
+        # the triangle).
+        self.triangle_size = 5
+
+
+    """
+    Calculate the Pascal number for the (row, column) cell, where row and column
+    are both 0-based. This is equivalent to calculating the Binomial coefficient
+    of (row choose column).
+    """
+    def _calculate_pascal_number(self, row, column):
+        num = math.factorial(row)
+        denom = math.factorial(column) * math.factorial(row - column)
+        return num / denom
+
 
     def _drawing_area_button_press_cb(self, widget, event, data = None):
         pass
 
 
     def _drawing_area_draw_cb(self, widget, ctx, data = None):
-        return False
+        # Default sizes (Cairo units).
+        padding = 10.0
+
+        # Widget allocation.
+        widget_height = widget.get_allocated_height()
+        base_width = widget.get_allocated_width() - 2.0 * padding
+        triangle_height = widget_height - 2.0 * padding
+        cell_width = base_width / self.triangle_size
+        cell_height = triangle_height / self.triangle_size
+
+        # Draw the triangle rows from the top down. The row_order is the number
+        # of cells in the row (increasing from 1 to triangle_size, inclusive).
+        row_order = 1
+        # X position of the first cell on the row
+        cell_start_x = padding + base_width / 2.0 - cell_width / 2.0
+
+        for row_index in range(self.triangle_size):
+            for column_index in range(row_order):
+                # Calculate the cell position. Add an offset every odd row so
+                # the triangle is balanced.
+                cell_x = cell_start_x + cell_width * column_index
+                cell_y = padding + cell_height * row_index
+
+                # Draw the cell and fill it.
+                ctx.rectangle(cell_x, cell_y, cell_width, cell_height)
+                ctx.set_source_rgb(0.0, 0.0, 0.0)
+                ctx.stroke_preserve()
+                ctx.set_source_rgb(1.0, 1.0, 1.0)
+                ctx.fill()
+
+                # Write its number.
+                cell_number = self._calculate_pascal_number(row_index,
+                                                            column_index)
+                extents = ctx.text_extents(str(cell_number))
+                ctx.move_to(cell_x + (cell_width - extents[2]) / 2.0,
+                            cell_y + (cell_height - extents[3]) / 2.0)
+                ctx.set_source_rgb(0.0, 0.0, 0.0)
+                ctx.show_text(str(cell_number))
+
+            cell_start_x -= cell_width / 2.0
+            row_order += 1
+
+        return True