def getProjectionMatrix(forward, up = pgl.Vector3(0,0,1)):
forward.normalize()
up.normalize();
side = pgl.cross(up, forward);
side.normalize();
up = pgl.cross(forward, side);
up.normalize();
return pgl.Matrix3(side, up, forward).inverse()
def lookAt(self, eyePosition3D, center3D, upVector3D):
forward = Vector3(center3D) - Vector3(eyePosition3D)
forward.normalize()
upVector3D = Vector3(upVector3D)
upVector3D.normalize()
side = cross(forward, upVector3D)
side.normalize()
up = cross(side, forward)
up.normalize()
m = Matrix4(side, up, forward, -eyePosition3D)
self.worldToCamera = m.inverse()
return m
def project3Dto2D(p3list):
v01 = Vector3((p3list[1][0] - p3list[0][0]), (p3list[1][1] - p3list[0][1]), (p3list[1][2] - p3list[0][2]))
v12 = Vector3((p3list[2][0] - p3list[1][0]), (p3list[2][1] - p3list[1][1]), (p3list[2][2] - p3list[1][2]))
vn = pgl.cross(v01, v12)
p2s = []
# cosTheta = A dot B/(|A|*|B|) => if A dot B ==0, then Theta == 90
# if polygon not || y axis, project it to the y=0 plane
if pgl.dot(vn, Vector3(0, 1, 0)) != 0:
for i in range(len(p3list)):
v = p3list[i][0], p3list[i][2]
p2s.append(v)
else:
# if polygon || y axis and z axis (it will perpendicular x axis), project it to the x=0 plane
# if polygon || y axis and x axis (it will perpendicular z axis), project it to the z=0 plane
# if polygon || y axis, not || x and z (it will not perpendicular z and x
# axis), project it to the z=0 plane (or x=0 plane)
if pgl.dot(vn, Vector3(0, 0, 1)) == 0:
for i in range(len(p3list)):
v = p3list[i][1], p3list[i][2]
p2s.append(v)
else:
for i in range(len(p3list)):
v = p3list[i][0], p3list[i][1]
p2s.append(v)
return p2s
def project3Dto2D(p3list):
v01 = Vector3((p3list[1][0] - p3list[0][0]), (p3list[1][1] - p3list[0][1]),
(p3list[1][2] - p3list[0][2]))
v12 = Vector3((p3list[2][0] - p3list[1][0]), (p3list[2][1] - p3list[1][1]),
(p3list[2][2] - p3list[1][2]))
vn = pgl.cross(v01, v12)
p2s = []
# cosTheta = A dot B/(|A|*|B|) => if A dot B ==0, then Theta == 90
# if polygon not || y axis, project it to the y=0 plane
if pgl.dot(vn, Vector3(0, 1, 0)) != 0:
for i in range(len(p3list)):
v = p3list[i][0], p3list[i][2]
p2s.append(v)
else:
# if polygon || y axis and z axis (it will perpendicular x axis), project it to the x=0 plane
# if polygon || y axis and x axis (it will perpendicular z axis), project it to the z=0 plane
# if polygon || y axis, not || x and z (it will not perpendicular z and x
# axis), project it to the z=0 plane (or x=0 plane)
if pgl.dot(vn, Vector3(0, 0, 1)) == 0:
for i in range(len(p3list)):
v = p3list[i][1], p3list[i][2]
p2s.append(v)
else:
for i in range(len(p3list)):
v = p3list[i][0], p3list[i][1]
p2s.append(v)
return p2s
def _set_axis(self, axis):
"""Property helper method.
"""
if axis != self._axis:
self._axis = axis
rotation_axis = pgl.cross(pgl.Vector3.OZ, self._axis)
rotation_angle = pgl.angle(self._axis, pgl.Vector3.OZ)
self.rotated.axis = rotation_axis
self.rotated.angle = rotation_angle
def _set_axis( self, axis ):
"""Property helper method.
"""
if axis != self._axis:
self._axis = axis
rotation_axis = pgl.cross( pgl.Vector3.OZ, self._axis )
rotation_angle = pgl.angle( self._axis, pgl.Vector3.OZ )
self.rotated.axis = rotation_axis
self.rotated.angle = rotation_angle
def __init__(self,
pos=ASHAPE3D_STANDARD_POS,
axis=ASHAPE3D_STANDARD_AXIS,
roll=ASHAPE3D_STANDARD_ROLL,
scale=ASHAPE3D_STANDARD_SCALE,
material=ASHAPE3D_STANDARD_MATERIAL,
geometry=None,
**keys):
"""Default constructor.
Parameters:
pos : Vector3 convertable
pos of the object (look below),
axis : Vector3 convertable
main axis of the object, should be defined to describe the rotation. The Z of the primitive geometry
would point to axis,
roll : Real
Property: rotation of the object around main axis,
scale : Vector3 convertable
to use while resizing the object. While scaling the Z corresponds to main axis of the object,
material : pgl.Material
describes the appearance of the object,
geometry : pgl.Geometry
describes the geometry of the object.
"""
if not geometry:
raise Exception("AShape3D: geometry not defined.")
self.geometry = geometry
#TODO check for custom rotation, scale, transformation objects (shared between shapes)
self.scaled = pgl.Scaled(scale, self.geometry)
# roll related
self._roll = roll #: to keep internal roll
self.rolled = pgl.AxisRotated(pgl.Vector3.OZ, self._roll, self.scaled)
# axis related (even the object which do not have intuitive axis need to have predefined axis
self._axis = axis #: to keep internal axis vector
rotation_axis = pgl.cross(pgl.Vector3.OZ, self._axis)
rotation_angle = pgl.angle(self._axis, pgl.Vector3.OZ)
self.rotated = pgl.AxisRotated(rotation_axis, rotation_angle,
self.rolled)
# position related
self.translated = pgl.Translated(pos, self.rotated)
# apperance related
self.shape = pgl.Shape(self.translated, material)
def __init__( self, pos=ASHAPE3D_STANDARD_POS, axis=ASHAPE3D_STANDARD_AXIS, roll=ASHAPE3D_STANDARD_ROLL,
scale=ASHAPE3D_STANDARD_SCALE, material=ASHAPE3D_STANDARD_MATERIAL, geometry=None, **keys ):
"""Default constructor.
Parameters:
pos : Vector3 convertable
pos of the object (look below),
axis : Vector3 convertable
main axis of the object, should be defined to describe the rotation. The Z of the primitive geometry
would point to axis,
roll : Real
Property: rotation of the object around main axis,
scale : Vector3 convertable
to use while resizing the object. While scaling the Z corresponds to main axis of the object,
material : pgl.Material
describes the appearance of the object,
geometry : pgl.Geometry
describes the geometry of the object.
"""
if not geometry:
raise Exception( "AShape3D: geometry not defined." )
self.geometry = geometry
#TODO check for custom rotation, scale, transformation objects (shared between shapes)
self.scaled = pgl.Scaled( scale, self.geometry )
# roll related
self._roll = roll #: to keep internal roll
self.rolled = pgl.AxisRotated(pgl.Vector3.OZ, self._roll, self.scaled)
# axis related (even the object which do not have intuitive axis need to have predefined axis
self._axis = axis #: to keep internal axis vector
rotation_axis = pgl.cross( pgl.Vector3.OZ, self._axis )
rotation_angle = pgl.angle( self._axis, pgl.Vector3.OZ )
self.rotated = pgl.AxisRotated( rotation_axis, rotation_angle, self.rolled )
# position related
self.translated = pgl.Translated( pos, self.rotated )
# apperance related
self.shape = pgl.Shape( self.translated, material )
def _normal(ind, pts):
A, B, C = [pts[i] for i in ind]
n = pgl.cross(B - A, C - A)
return n.normed()
def _surf(ind, pts):
A, B, C = [pts[i] for i in ind]
return pgl.norm(pgl.cross(B - A, C - A)) / 2.0
def _normal(ind,pts):
A,B,C = [pts[i] for i in ind]
n = pgl.cross(B-A, C-A)
return n.normed()
def _surf(ind,pts):
A,B,C = [pts[i] for i in ind]
return pgl.norm(pgl.cross(B-A, C-A)) / 2.0
def _normal(mesh, iface):
A, B, C = [mesh.pointList[i] for i in mesh.indexAt(iface)]
n = pgl.cross(B - A, C - A)
return n.normed()
def _surf(mesh, iface):
A, B, C = [mesh.pointList[i] for i in mesh.indexAt(iface)]
return pgl.norm(pgl.cross(B - A, C - A)) / 2.0
def _surf(ind, pts):
from openalea.plantgl.all import norm, cross, Vector3
A, B, C = [Vector3(pts[i]) for i in ind]
return norm(cross(B - A, C - A)) / 2.0