球の頂点リストを使用してSphere面を作成するのではなく、Mayaで最初から作成しています。平面を作成し、通常の球の面と一致するように回転させる必要があります。
私のアイデアは、球の面の頂点間の中心角を水平方向と垂直方向に取得することでした。これはY軸に対しては機能しますが、回転を適用するとすぐにX顔の向きが失われます。
この画像では、球の面の1つをX軸上で意図的に回転させて、計算する必要のある回転の種類を示しています。実装はPythonで書かれているので、必要に応じてすべてのベクターメソッドにアクセスできます。この球体の実装は別の目的であるため、セットアップが少し奇妙に見える場合があることに注意してください。
import pymel.core as pm
import pymel.core.datatypes as dt
import pymel.util as util
degrees = util.arrays.degrees
cos = util.arrays.cos
sin = util.arrays.sin
atan2 = util.math.atan2
acos = util.math.acos
sqrt = util.math.sqrt
PI = util.arrays.pi
TWO_PI = PI * 2
def distance(x1, y1, z1, x2, y2, z2):
return sqrt( (x2 - x1) ** 2 + (y2 - y1) ** 2 + (z2 - z1) ** 2 )
# Sphere class
class Sphere():
# Initialise radius (float), subdivisionsAxis (int), subdivisionsHeight (int)
def __init__(self, radius = 10, subdivisionsAxis = 8, subdivisionsHeight = 8):
# Loop through each subdivision on y axis
for i in range(subdivisionsHeight):
if i == 0 or i == subdivisionsHeight - 1:
# Store the triangle vertices's in this list
data = self.generateSphereData(radius, subdivisionsAxis, subdivisionsHeight, i, 'triangle')
length = len(data) / 11
for j in range(length):
index = j * 11
x1 = data[index]
y1 = data[index + 1]
z1 = data[index + 2]
x2 = data[index + 3]
y2 = data[index + 4]
z2 = data[index + 5]
x3 = data[index + 6]
y3 = data[index + 7]
z3 = data[index + 8]
# Angle y
ay = data[index + 9]
# Angle z
az = data[index + 10]
v1 = dt.FloatVector(x1, y1, z1)
v2 = dt.FloatVector(x2, y2, z2)
v3 = dt.FloatVector(x3, y3, z3)
# Ignore the top and bottom triangles for now...
# pm.polyCreateFacet( p = [ v1, v2, v3 ] )
else:
# Store the quads vertices's in this list
data = self.generateSphereData(radius, subdivisionsAxis, subdivisionsHeight, i, 'quad')
length = len(data) / 14
for j in range(length):
index = j * 14
x1 = data[index]
y1 = data[index + 1]
z1 = data[index + 2]
x2 = data[index + 3]
y2 = data[index + 4]
z2 = data[index + 5]
x3 = data[index + 6]
y3 = data[index + 7]
z3 = data[index + 8]
x4 = data[index + 9]
y4 = data[index + 10]
z4 = data[index + 11]
# Angle y
ay = data[index + 12]
# Angle z
az = data[index + 13]
v1 = dt.FloatVector(x1, y1, z1)
v2 = dt.FloatVector(x2, y2, z2)
v3 = dt.FloatVector(x3, y3, z3)
v4 = dt.FloatVector(x4, y4, z4)
# Calculate centroid
cx = (x1 + x2 + x3 + x4) / 4
cy = (y1 + y2 + y3 + y4) / 4
cz = (z1 + z2 + z3 + z4) / 4
# Calculate the width and height
# Calculate dimensions for facet
tw = distance(x1, y1, z1, x4, y4, z4)
bw = distance(x2, y2, z2, x3, y3, z3)
w = tw if bw < tw else bw
h = distance(x2, y2, z2, x1, y1, z1)
# Calculate rotation of face
centroid = dt.FloatVector(cx, cy, cz)
mesh = pm.polyPlane(width=1, height=1, subdivisionsX=1, subdivisionsY=1, axis=(1, 0, 0))
mesh[0].setTranslation(centroid)
mesh[0].setRotation([0, degrees(-ay), 0])
pm.spaceLocator(p=v1)
pm.spaceLocator(p=v2)
pm.spaceLocator(p=v3)
pm.spaceLocator(p=v4)
# pm.polyCreateFacet( p = [ v1, v2, v3, v4 ] )
# Generate a vertex list of the spheres current subdivision height level
# Arguments: radius (float), subdivisionsAxis (int), subdivisionsHeight (int), index (int), polygonType (string)
def generateSphereData(self, radius, subdivisionsAxis, subdivisionsHeight, index, polygonType):
positions = []
if polygonType == 'triangle':
for i in range(subdivisionsAxis):
# If were generating the top triangles we need the triangle base to
# Be at the previous subdivision level, so change the index to index - 1
if index < subdivisionsHeight:
nextIndex = index + 1
else:
nextIndex = index - 1
if i < subdivisionsAxis - 1:
j = i + 1
else:
j = 0
# Top vertex
r1 = radius * sin(index * (PI / subdivisionsAxis))
x1 = r1 * cos(i * (TWO_PI / subdivisionsAxis))
y1 = radius * cos(index * (PI / subdivisionsHeight))
z1 = r1 * sin(i * (TWO_PI / subdivisionsAxis))
# Left vertex
r2 = radius * sin(nextIndex * (PI / subdivisionsAxis))
x2 = r2 * cos(i * (TWO_PI / subdivisionsAxis))
y2 = radius * cos(nextIndex * (PI / subdivisionsHeight))
z2 = r2 * sin(i * (TWO_PI / subdivisionsAxis))
# Right vertex
x3 = r2 * cos(j * (TWO_PI / subdivisionsAxis))
y3 = radius * cos(nextIndex * (PI / subdivisionsHeight))
z3 = r2 * sin(j * (TWO_PI / subdivisionsAxis))
# Calculate angles
ay = 0
az = 0
positions += [x1, y1, z1, x2, y2, z2, x3, y3, z3, ay, az]
elif polygonType == 'quad':
nextIndex = index + 1
for i in range(subdivisionsAxis):
if i < subdivisionsAxis - 1:
j = i + 1
else:
j = 0
# Bottom y
r1 = radius * sin(index * (PI / subdivisionsAxis))
y1 = radius * cos(index * (PI / subdivisionsHeight))
# Top y
r2 = radius * sin(nextIndex * (PI / subdivisionsAxis))
y2 = radius * cos(nextIndex * (PI / subdivisionsHeight))
# Top left vertex
x1 = r2 * cos(i * (TWO_PI / subdivisionsAxis))
z1 = r2 * sin(i * (TWO_PI / subdivisionsAxis))
# Bottom left vertex
x2 = r1 * cos(i * (TWO_PI / subdivisionsAxis))
z2 = r1 * sin(i * (TWO_PI / subdivisionsAxis))
# Bottom right vertex
x3 = r1 * cos(j * (TWO_PI / subdivisionsAxis))
z3 = r1 * sin(j * (TWO_PI / subdivisionsAxis))
# Top right vertex
x4 = r2 * cos(j * (TWO_PI / subdivisionsAxis))
z4 = r2 * sin(j * (TWO_PI / subdivisionsAxis))
# Calculate angles
ay1 = i * (TWO_PI / subdivisionsAxis)
ay2 = j * (TWO_PI / subdivisionsAxis)
ay = ay1 + ((ay2 - ay1) / 2)
az1 = index * (PI / subdivisionsHeight)
az2 = nextIndex * (PI / subdivisionsHeight)
az = az1 + ((az2 - az1) / 2)
positions += [x1, y2, z1, x2, y1, z2, x3, y1, z3, x4, y2, z4, ay, az]
return positions
Sphere(20, 8, 8)