def calculateEndPerpendiculars(self, start, control0, control1, end):
unitC00 = VectMath.unitvect(
[control0[0] - start[0], control0[1] - start[1]])
#unitControl00 = [self.startPos[0]+(10*unitC00[0]),self.startPos[1]+(10*unitC00[1])]
perpUnitStartLeft = [
start[0] + (10 * unitC00[1]), start[1] - (10 * unitC00[0])
]
perpUnitStartRright = [
start[0] - (10 * unitC00[1]), start[1] + (10 * unitC00[0])
]
unitC01 = VectMath.unitvect(
[control1[0] - end[0], control1[1] - end[1]])
#unitControl01 = [self.endPos[0]+(10*unitC01[0]),self.endPos[1]+(10*unitC01[1])]
perpUnitEndLeft = [
end[0] - (10 * unitC01[1]), end[1] + (10 * unitC01[0])
]
perpUnitEndRight = [
end[0] + (10 * unitC01[1]), end[1] - (10 * unitC01[0])
]
return [
perpUnitStartLeft, perpUnitStartRright, perpUnitEndLeft,
perpUnitEndRight
]
def calculateUnitPerpendiculars(self,start,control0,control1,end):
unitC00 = VectMath.unitvect([control0[0]-start[0],control0[1]-start[1]])
perpUnitStartLeft = [0+unitC00[1],0-unitC00[0]]
perpUnitStartRright = [0-unitC00[1],0+unitC00[0]]
unitC01 = VectMath.unitvect([control1[0]-end[0],control1[1]-end[1]])
perpUnitEndLeft = [0-unitC01[1],0+unitC01[0]]
perpUnitEndRight = [0+unitC01[1],0-unitC01[0]]
return [perpUnitStartLeft,perpUnitStartRright,perpUnitEndLeft,perpUnitEndRight]
def calculateEndPerpendiculars(start,control0,control1,end):
unitC00 = VectMath.unitvect([control0[0]-start[0],control0[1]-start[1]])
#unitControl00 = [self.startPos[0]+(10*unitC00[0]),self.startPos[1]+(10*unitC00[1])]
perpUnitStartLeft = [start[0]+(10*unitC00[1]),start[1]-(10*unitC00[0])]
perpUnitStartRright = [start[0]-(10*unitC00[1]),start[1]+(10*unitC00[0])]
unitC01 = VectMath.unitvect([control1[0]-end[0],control1[1]-end[1]])
#unitControl01 = [self.endPos[0]+(10*unitC01[0]),self.endPos[1]+(10*unitC01[1])]
perpUnitEndLeft = [end[0]-(10*unitC01[1]),end[1]+(10*unitC01[0])]
perpUnitEndRight = [end[0]+(10*unitC01[1]),end[1]-(10*unitC01[0])]
return [perpUnitStartLeft,perpUnitStartRright,perpUnitEndLeft,perpUnitEndRight]
def calculateUnitPerpendiculars(self, start, control0, control1, end):
unitC00 = VectMath.unitvect(
[control0[0] - start[0], control0[1] - start[1]])
perpUnitStartLeft = [0 + unitC00[1], 0 - unitC00[0]]
perpUnitStartRright = [0 - unitC00[1], 0 + unitC00[0]]
unitC01 = VectMath.unitvect(
[control1[0] - end[0], control1[1] - end[1]])
perpUnitEndLeft = [0 - unitC01[1], 0 + unitC01[0]]
perpUnitEndRight = [0 + unitC01[1], 0 - unitC01[0]]
return [
perpUnitStartLeft, perpUnitStartRright, perpUnitEndLeft,
perpUnitEndRight
]
def calculatePerpendiculars(start,end):
unit = VectMath.unitvect([end[0]-start[0],end[1]-start[1]])
perpUnitStartLeft = [start[0]+(10*unit[1]),start[1]-(10*unit[0])]
perpUnitStartRright = [start[0]-(10*unit[1]),start[1]+(10*unit[0])]
perpUnitEndLeft = [end[0]+(10*unit[1]),end[1]-(10*unit[0])]
perpUnitEndRight = [end[0]-(10*unit[1]),end[1]+(10*unit[0])]
return [perpUnitStartLeft,perpUnitStartRright,perpUnitEndLeft,perpUnitEndRight]
def GetBezierPoint(points, t):
"""EXPLANATION:
The formula for a point on the bezier curve defined by four points (points[0:3]) at a given value of t is as follows:
B(t) = ((1-t)^3 * points[0]) + (3 * (1-t)^2 * t * points[1]) + (3 * (1-t) * t^2 * points[2]) + (t^3 * points[3])
(Where 0 <= t <= 1.)
Here, the formula has been split into the four component parts, each returning a vactor:
-part1 = (1-t)^3 * points[0]
-part2 = 3 * (1-t)^2 * t * points[1]
-part3 = 3 * (1-t) * t^2 * points[2]
-part4 = t^3 * points[3]
These vectors are then added using the function fourpointsum() to give the final value for B(t).
"""
part1 = VectMath.vectmult(cube(1.0 - t), points[0])
part2 = VectMath.vectmult((3 * sqr(1.0 - t) * t), points[1])
part3 = VectMath.vectmult((3 * (1.0 - t) * sqr(t)), points[2])
part4 = VectMath.vectmult(cube(t), points[3])
return VectMath.fourpointsum(part1, part2, part3, part4)
