[Bf-extensions-cvs] SVN commit: /data/svn/bf-extensions [2102] trunk/py/scripts/addons/modules/ curve_utils.py: add a second experimental method of solving bezier splines, by Vincent Tan.
Campbell Barton
ideasman42 at gmail.com
Wed Jul 6 19:08:24 CEST 2011
Revision: 2102
http://projects.blender.org/scm/viewvc.php?view=rev&root=bf-extensions&revision=2102
Author: campbellbarton
Date: 2011-07-06 17:08:23 +0000 (Wed, 06 Jul 2011)
Log Message:
-----------
add a second experimental method of solving bezier splines, by Vincent Tan.
Modified Paths:
--------------
trunk/py/scripts/addons/modules/curve_utils.py
Modified: trunk/py/scripts/addons/modules/curve_utils.py
===================================================================
--- trunk/py/scripts/addons/modules/curve_utils.py 2011-07-06 15:46:51 UTC (rev 2101)
+++ trunk/py/scripts/addons/modules/curve_utils.py 2011-07-06 17:08:23 UTC (rev 2102)
@@ -361,13 +361,72 @@
self.calc_all()
- def bezier_solve(self):
+ def bezier_solve_(self):
""" Calculate bezier handles,
assume the splines have been broken up.
-
+ http://polymathprogrammer.com/
"""
+ p1 = self.points[0]
+ p2 = self.points[-1]
+
+ line_ix_p1 = self.points[len(self.points) // 3]
+ line_ix_p2 = self.points[int((len(self.points) / 3) * 2)]
+
+ u = 1 / 3
+ v = 2 / 3
+
+ p0x, p0y, p0z = p1.co
+ p1x, p1y, p1z = line_ix_p1.co
+ p2x, p2y, p2z = line_ix_p2.co
+ p3x, p3y, p3z = p2.co
+
+ ui = 1.0 - u
+ vi = 1.0 - v
+ u_p3 = u * u * u
+ v_p3 = v * v * v
+ ui_p3 = ui * ui * ui
+ vi_p3 = vi * vi * vi
+
+
+ # --- snip
+
+ q1 = Vector()
+ q2 = Vector()
+
+ pos = Vector(), Vector(), Vector(), Vector()
+
+ a = 3.0 * ui * ui * u
+ b = 3.0 * ui * u * u
+ c = 3.0 * vi * vi * v
+ d = 3.0 * vi * v * v
+ det = a * d - b * c
+
+ if det == 0.0:
+ assert(0)
+ return 0
+
+ q1.x = p1x - (ui_p3 * p0x + u_p3 * p3x)
+ q1.y = p1y - (ui_p3 * p0y + u_p3 * p3y)
+ q1.z = p1z - (ui_p3 * p0z + u_p3 * p3z)
+
+ q2.x = p2x - (vi_p3 * p0x + v_p3 * p3x)
+ q2.y = p2y - (vi_p3 * p0y + v_p3 * p3y)
+ q2.z = p2z - (vi_p3 * p0z + v_p3 * p3z)
+
+ pos[1].x = (d * q1.x - b * q2.x) / det
+ pos[1].y = (d * q1.y - b * q2.y) / det
+ pos[1].z = (d * q1.z - b * q2.z) / det
+
+ pos[2].x = ((-c) * q1.x + a * q2.x) / det
+ pos[2].y = ((-c) * q1.y + a * q2.y) / det
+ pos[2].z = ((-c) * q1.z + a * q2.z) / det
+
+ self.handle_left = pos[1]
+ self.handle_right = pos[2]
+
+ def bezier_solve(self):
from mathutils.geometry import (intersect_point_line,
intersect_line_line,
)
@@ -391,58 +450,19 @@
# visualize_line(p2.co, l2_co)
# picking 1/2 and 2/3'rds works best
- line_ix_p1 = self.points[len(self.points) // 3]
+ line_ix_p1 = self.points[int(len(self.points) * (1.0 / 3.0))]
line_ix_p1_co, line_ix_p1_no = line_ix_p1.co, line_ix_p1.no
- line_ix_p2 = self.points[int((len(self.points) / 3) * 2)]
+ line_ix_p2 = self.points[int(len(self.points) * (2.0 / 3.0))]
line_ix_p2_co, line_ix_p2_no = line_ix_p2.co, line_ix_p2.no
- if line_ix_p1_co is None:
- line_ix_p1_co, line_ix_p1_no, line_ix_p1 = \
- p1.next.co, p1.next.no, p1.next
- if line_ix_p2_co is None:
- line_ix_p2_co, line_ix_p2_no, line_ix_p2 = \
- p2.prev.co, p2.prev.no, p2.prev
+ # used to seek for the upper most point but this gives mostly
+ # as good results
+ p1_apex_co = self.points[int(len(self.points) * (1.0 / 3.0) * 0.75)].co
+ p2_apex_co = self.points[int(len(self.points) * (1.0 - (1.0 / 3.0) * 0.75))].co
- # vis_circle_object(line_ix_p1_co)
- # vis_circle_object(line_ix_p2_co)
-
- l1_max = 0.0
- p1_apex_co = None
- p = self.points[1]
- while p and (not p.is_joint) and p != line_ix_p1:
- ix = intersect_point_line(p.co, p1.co, l1_co)[0]
- length = (ix - p.co).length
- if length > l1_max:
- l1_max = length
- p1_apex_co = p.co
- p = p.next
-
- l2_max = 0.0
- p2_apex_co = None
- p = self.points[-2]
- while p and (not p.is_joint) and p != line_ix_p2:
- ix = intersect_point_line(p.co, p2.co, l2_co)[0]
- length = (ix - p.co).length
- if length > l2_max:
- l2_max = length
- p2_apex_co = p.co
- p = p.prev
-
- if p1_apex_co is None:
- p1_apex_co = p1.next.co
- if p2_apex_co is None:
- p2_apex_co = p2.prev.co
-
l1_tan = (p1.no - p1.no.project(l1_no)).normalized()
l2_tan = -(p2.no - p2.no.project(l2_no)).normalized()
- # values are good!
- #~ visualize_line(p1.co, p1.co + l1_tan)
- #~ visualize_line(p2.co, p2.co + l2_tan)
-
- #~ visualize_line(p1.co, p1.co + l1_no)
- #~ visualize_line(p2.co, p2.co + l2_no)
-
# calculate bias based on the position of the other point allong
# the tangent.
@@ -454,7 +474,7 @@
from math import pi
# This could be tweaked but seems to work well
- fac_fac = (p1.co - p2.co).length * p1.no.angle(l2_no_ref) / pi
+ fac_fac = (p1.co - p2.co).length * p1.no.angle(l2_no_ref) / (pi * 1.0)
fac_1 = intersect_point_line(p2_apex_co,
p1.co,
@@ -474,14 +494,14 @@
self.handle_left = h1
self.handle_right = h2
- '''
+ """
visualize_line(p1.co, p1_apex_co)
visualize_line(p1_apex_co, p2_apex_co)
visualize_line(p2.co, p2_apex_co)
visualize_line(p1.co, p2.co)
- '''
+ """
- def bezier_error(self, error_max=-1.0, test_count=8):
+ def bezier_error(self, error_max=-1.0, test_count=16):
from mathutils.geometry import interpolate_bezier
test_points = interpolate_bezier(self.points[0].co,
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