Add quadratic bezier curves

Author: sseemayer

py2d/Bezier.py

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+"""Bezier curve tools.
+
+All functions in this module assume the following naming:
+
+         C1           
+         ____
+        /    \      P2
+        |     \______|          
+	P1             
+                       C2
+
+A bezier curve is formed between two points P1 and P2, with curve direction coming from control points Ci.
+
+References:
+	www.caffeineowl.com/graphics/2d/vectorial/bezierintro.htm
+"""
+
+from py2d.Math import Vector, distance_point_line
+
+
+def point_on_cubic_bezier(p1,p2,c1,c2,t):
+	"""Find a point on a cubic bezier curve, i.e. a bezier curve with two control points.
+	
+	@type p1: Vector
+	@param p1: Start point of the curve
+	
+	@type p2: Vector
+	@param p2: Stop point of the curve
+
+	@type c1: Vector
+	@param c1: Control point for point A
+
+	@type c2: Vector
+	@param c2: Control point for point B
+
+	@type t: float
+	@param t: Relative position on the bezier curve between 0 and 1
+	"""
+
+	one_minus_t = 1.0 - t
+	one_minus_t_2 = one_minus_t * one_minus_t
+	one_minus_t_3 = one_minus_t_2 * one_minus_t
+
+	t_2 = t * t
+	t_3 = t_2 * t
+
+	return p1 * one_minus_t_3 + c1 * (3 * one_minus_t_2 * t) + c2 * (3 * one_minus_t * t_2) + p2 * t_3
+
+
+def subdivide_cubic_bezier(p1,p2,c1,c2,t):
+	"""Subdivide a cubic bezier curve and return the point on the curve plus new control points"""
+
+	one_minus_t = 1.0 - t
+
+	a = p1 * one_minus_t + c1 * t
+	b = c1 * one_minus_t + c2 * t
+	c = c2 * one_minus_t + p2 * t
+
+	m = a * one_minus_t + b * t 
+	n = b * one_minus_t + c * t
+
+	p = m * one_minus_t + n * t
+
+	return a,m,p,n,c
+
+
+def flatten_cubic_bezier(p1,p2,c1,c2, max_divisions=None, max_flatness=0.1):
+	out = []
+
+	if not __is_flat(max_divisions, max_flatness, __bezier_flatness(p1,p2,c1,c2)):
+		a,m,p,n,c = subdivide_cubic_bezier(p1,p2,c1,c2,0.5)
+
+		md_rec = max_divisions - 1 if max_divisions else None
+
+		out.extend(flatten_cubic_bezier(p1,p,a,m, md_rec, max_flatness))
+		out.append(p)
+		out.extend(flatten_cubic_bezier(p,p2,n,c, md_rec, max_flatness))
+
+	return out
+
+def __is_flat(max_divisions, max_flatness, flatness):
+	return (max_divisions == 0) or (max_flatness != None and flatness <= max_flatness)
+
+def __bezier_flatness(p1,p2, *c):
+	return min(distance_point_line(cp, p1, p2) for cp in c)

��py2d/examples/Bezier.py

@@ -0,0 +1,74 @@
+import pygame
+from pygame.locals import *
+
+from py2d.Bezier import *
+from py2d.Math import *
+import py2d.examples.Main
+
+SELECTION_DISTANCE = 20
+
+class Bezier(py2d.examples.Main.Example):
+	"""Bezier curve sample
+	
+	Draw around end and control points of the bezier curve.
+
+	Key mappings:
+	  MOUSE1: Drag points
+
+	Have fun!
+	"""
+
+	def __init__(self, runner):
+		self.runner = runner
+		self.title = "Simple Drawing"
+
+		self.p1 = Vector(200,400)
+		self.p2 = Vector(400,400)
+		self.c1 = Vector(500,50)
+		self.c2 = Vector(100,50)
+
+
+		self.points = ( ('P1', (255,0,0), self.p1),
+				('P2', (255,0,0), self.p2),
+				('C1', (0,255,0), self.c1),
+				('C2', (0,255,0), self.c2) )
+
+		self.sel_point = None
+
+	def update(self, time_elapsed):
+		pass
+
+	def render(self):
+	
+		pygame.draw.line(self.runner.screen, 0x006600, self.p1.as_tuple(), self.c1.as_tuple())
+		pygame.draw.line(self.runner.screen, 0x006600, self.p2.as_tuple(), self.c2.as_tuple())
+
+		for label, color, pos in self.points:
+			self.draw_point(pos, color, label)
+
+		bezier = [self.p1] + flatten_cubic_bezier(self.p1, self.p2, self.c1, self.c2) + [self.p2]
+
+		pygame.draw.lines(self.runner.screen, 0xffffff, False, [p.as_tuple() for p in bezier], 2)
+
+		if self.sel_point:
+			pygame.draw.ellipse(self.runner.screen, 0xfff00, pygame.Rect( (self.sel_point.x - 4, self.sel_point.y - 4), (8,8)) , 1)
+
+	def draw_point(self, p, color, label=None):
+		pygame.draw.ellipse(self.runner.screen, color, pygame.Rect(p.as_tuple(), (2,2)))
+		if label:
+			self.runner.screen.blit(self.runner.font.render(label, False, color), p.as_tuple())
+
+	def mouse_down(self, pos, button):
+		if button == 1:
+			mouse = Vector(*pos)
+
+			nearest = min(self.points, key=lambda p: (p[2]-mouse).length)
+
+			if (nearest[2] - mouse).length_squared <= SELECTION_DISTANCE:
+				self.sel_point = nearest[2]
+			else:
+				self.sel_point = None
+
+	def mouse_move(self, pos, rel, buttons):
+		if buttons[0] and self.sel_point:
+			self.sel_point.x, self.sel_point.y = pos