def bezier3dCrv(crv3d, t):
dim = crv3d.dim
degree = crv3d.degree
pntLst = crv3d.controlPnt
type = crv3d.curveType
if dim != 3:
return None
if len(pntLst) != degree + 1:
return None
for i in range(degree):
tempPnt = np.array([])
for j in range(len(pntLst) - 1):
x = t * pntLst[j + 1].x + (1 - t) * pntLst[j].x
y = t * pntLst[j + 1].y + (1 - t) * pntLst[j].y
z = t * pntLst[j + 1].z + (1 - t) * pntLst[j].z
pnt = point(x, y, z)
tempPnt = np.append(tempPnt, pnt)
pntLst = tempPnt
return pntLst[0]
def extendBezierCrv(curveInfo, t):
pntLst = curveInfo.controlPnt
if t < 0:
pntLst = pntLst[::-1]
t = np.fabs(t)
degree = curveInfo.degree
extendCrv = np.array([])
if degree + 1 != len(pntLst):
return None
for i in range(degree):
if i == 0:
x = pntLst[0].x
y = pntLst[0].y
pnt = point(x, y)
extendCrv = np.append(extendCrv, pnt)
tempPnt = np.array([])
for j in range(len(pntLst) - 1):
x = pntLst[j].x + 1 / (t - 1) * (pntLst[j + 1].x - pntLst[j].x)
y = pntLst[j].y + 1 / (t - 1) * (pntLst[j + 1].y - pntLst[j].y)
pnt = point(x, y)
tempPnt = np.append(tempPnt, pnt)
if j == 0:
extendCrv = np.append(extendCrv, pnt)
pntLst = tempPnt
return extendCrv
def upgradeBezierDegree(curveInfo):
pntLst = curveInfo.controlPnt
degree = curveInfo.degree
crvPntLst = np.array([])
crvPntLst = np.append(crvPntLst, pntLst[0])
for i in range(len(pntLst) - 1):
alpha = (i + 1) / (degree + 1)
x = (pntLst[i].x * alpha + pntLst[i + 1].x) / (1 + alpha)
y = (pntLst[i].y * alpha + pntLst[i + 1].y) / (1 + alpha)
pnt = point(x, y)
crvPntLst = np.append(crvPntLst, pnt)
crvPntLst = np.append(crvPntLst, pntLst[len(pntLst) - 1])
newCrveInfo = nurbCurve(crvPntLst, degree + 1)
return newCrveInfo
tempPnt = np.array([])
for j in range(len(pntLst) - 1):
x = t * pntLst[j + 1].x + (1 - t) * pntLst[j].x
y = t * pntLst[j + 1].y + (1 - t) * pntLst[j].y
z = t * pntLst[j + 1].z + (1 - t) * pntLst[j].z
pnt = point(x, y, z)
tempPnt = np.append(tempPnt, pnt)
pntLst = tempPnt
return pntLst[0]
if __name__ == "__main__":
pnt1 = point(-41.88438, 41.26041, 49.91586)
pnt2 = point(-73.06837, 13.91201, 87.07949)
pnt3 = point(-39.28571, -33.41261, 46.81889)
controlPnt = np.array([pnt1, pnt2, pnt3])
crv3d = nurbCurve(controlPnt, 2, 3)
pnt = bezier3dCrv(crv3d, 0.1)
print(pnt.x, ',', pnt.y, ',', pnt.z)
pnt = bezier3dCrv(crv3d, 0.2)
print(pnt.x, ',', pnt.y, ',', pnt.z)
pnt = bezier3dCrv(crv3d, 0.3)
print(pnt.x, ',', pnt.y, ',', pnt.z)
def decasteljaus(curveInfo, t):
pntLst = curveInfo.controlPnt
n = curveInfo.degree
if n + 1 != len(pntLst):
return None
if t < 0:
return None
tempPnt = np.array([])
firstDer = None
pnt = None
firstCurve = np.array([])
secondCurve = np.array([])
firstCurve = np.append(firstCurve, pntLst[0])
secondCurve = np.append(secondCurve, pntLst[len(pntLst) - 1])
secondDer = None
for i in range(n):
if i == n - 1:
firstDer_x = pntLst[1].x - pntLst[0].x
firstDer_y = pntLst[1].y - pntLst[0].y
firstDer_x = firstDer_x * n
firstDer_y = firstDer_y * n
firstDer = point(firstDer_x, firstDer_y)
x = t * pntLst[1].x + (1 - t) * pntLst[0].x
y = t * pntLst[1].y + (1 - t) * pntLst[0].y
pnt = point(x, y)
firstCurve = np.append(firstCurve, pnt)
secondCurve = np.append(secondCurve, pnt)
else:
if n >= 2 and i == n - 2:
secondDer_x = pntLst[2].x - 2 * pntLst[1].x + pntLst[0].x
secondDer_y = pntLst[2].y - 2 * pntLst[1].y + pntLst[0].y
secondDer_x = n * (n - 1) * secondDer_x
secondDer_y = n * (n - 1) * secondDer_y
secondDer = point(secondDer_x, secondDer_y)
for j in range(len(pntLst) - 1):
x = t * pntLst[j + 1].x + (1 - t) * pntLst[j].x
y = t * pntLst[j + 1].y + (1 - t) * pntLst[j].y
pnt = point(x, y)
tempPnt = np.append(tempPnt, pnt)
if j == 0:
firstCurve = np.append(firstCurve, pnt)
if j == len(pntLst) - 2:
secondCurve = np.append(secondCurve, pnt)
pntLst = tempPnt
tempPnt = np.array([])
secondCurve = secondCurve[::-1]
return pnt, firstDer, secondDer, firstCurve, secondCurve
for i in range(len(pntLst) - 1):
alpha = (i + 1) / (degree + 1)
x = (pntLst[i].x * alpha + pntLst[i + 1].x) / (1 + alpha)
y = (pntLst[i].y * alpha + pntLst[i + 1].y) / (1 + alpha)
pnt = point(x, y)
crvPntLst = np.append(crvPntLst, pnt)
crvPntLst = np.append(crvPntLst, pntLst[len(pntLst) - 1])
newCrveInfo = nurbCurve(crvPntLst, degree + 1)
return newCrveInfo
if __name__ == "__main__":
pnt1 = point(0, 0)
pnt2 = point(0, 100)
pnt3 = point(100, 100)
pnt4 = point(100, 0)
controlPnt = np.array([pnt1, pnt2, pnt3, pnt4])
curveInfo = bezier(3, controlPnt)
extendCrv = extendBezierCrv(curveInfo, 1.5)
print(extendCrv)
extendCrv = extendBezierCrv(curveInfo, -1.5)
print(extendCrv)
upgradeCrv = upgradeBezierDegree(curveInfo)