def getSphere(ndiv=3, radius=1.0):
# Example taken from the Red book, end of chaper 2.
# Define constants
X = 0.525731112119133606
Z = 0.850650808352039932
# Creta vdata
vdata = Pointset(3)
app = vdata.append
app(-X, 0.0, Z); app(X, 0.0, Z); app(-X, 0.0, -Z); app(X, 0.0, -Z)
app(0.0, Z, X); app(0.0, Z, -X); app(0.0, -Z, X); app(0.0, -Z, -X)
app(Z, X, 0.0); app(-Z, X, 0.0); app(Z, -X, 0.0); app(-Z, -X, 0.0)
# Create faces
tindices = [
[0,4,1], [0,9,4], [9,5,4], [4,5,8], [4,8,1],
[8,10,1], [8,3,10], [5,3,8], [5,2,3], [2,7,3],
[7,10,3], [7,6,10], [7,11,6], [11,0,6], [0,1,6],
[6,1,10], [9,0,11], [9,11,2], [9,2,5], [7,2,11] ]
tindices = np.array(tindices, dtype=np.uint32)
# Init vertex array
vertices = Pointset(3)
# Define function to recursively create vertices and normals
def drawtri(a, b, c, div):
if (div<=0):
vertices.append(a)
vertices.append(b)
vertices.append(c)
else:
ab = Point(0,0,0)
ac = Point(0,0,0)
bc = Point(0,0,0)
for i in range(3):
ab[i]=(a[i]+b[i])/2.0;
ac[i]=(a[i]+c[i])/2.0;
bc[i]=(b[i]+c[i])/2.0;
ab = ab.normalize(); ac = ac.normalize(); bc = bc.normalize()
drawtri(a, ab, ac, div-1)
drawtri(b, bc, ab, div-1)
drawtri(c, ac, bc, div-1)
drawtri(ab, bc, ac, div-1)
# Create vertices
for i in range(20):
drawtri( vdata[int(tindices[i][0])],
vdata[int(tindices[i][1])],
vdata[int(tindices[i][2])],
ndiv )
# Create normals and scale vertices
normals = vertices.copy()
vertices *= radius
# Done
return vertices, normals
def getSphereWithFaces(ndiv=3, radius=1.0):
# Example taken from the Red book, end of chaper 2.
# Define constants
X = 0.525731112119133606
Z = 0.850650808352039932
# Creta vdata
vdata = Pointset(3)
app = vdata.append
app(-X, 0.0, Z)
app(X, 0.0, Z)
app(-X, 0.0, -Z)
app(X, 0.0, -Z)
app(0.0, Z, X)
app(0.0, Z, -X)
app(0.0, -Z, X)
app(0.0, -Z, -X)
app(Z, X, 0.0)
app(-Z, X, 0.0)
app(Z, -X, 0.0)
app(-Z, -X, 0.0)
# Create faces
tindices = [[0, 4, 1], [0, 9, 4], [9, 5, 4], [4, 5, 8], [4, 8, 1],
[8, 10, 1], [8, 3, 10], [5, 3, 8], [5, 2, 3], [2, 7, 3],
[7, 10, 3], [7, 6, 10], [7, 11, 6], [11, 0, 6], [0, 1, 6],
[6, 1, 10], [9, 0, 11], [9, 11, 2], [9, 2, 5], [7, 2, 11]]
tindices = np.array(tindices, dtype=np.uint32)
# Init vertex array with existing points, init faces as empty list
vertices = vdata.copy()
faces = []
# Define function to recursively create vertices and normals
def drawtri(ia, ib, ic, div):
a, b, c = vertices[ia], vertices[ib], vertices[ic]
if (div <= 0):
# Store faces here
faces.extend([ia, ib, ic])
else:
# Create new points
ab = Point(0, 0, 0)
ac = Point(0, 0, 0)
bc = Point(0, 0, 0)
for i in range(3):
ab[i] = (a[i] + b[i]) / 2.0
ac[i] = (a[i] + c[i]) / 2.0
bc[i] = (b[i] + c[i]) / 2.0
ab = ab.normalize()
ac = ac.normalize()
bc = bc.normalize()
# Add new points
i_offset = len(vertices)
vertices.append(ab)
vertices.append(ac)
vertices.append(bc)
iab, iac, ibc = i_offset + 0, i_offset + 1, i_offset + 2
#
drawtri(ia, iab, iac, div - 1)
drawtri(ib, ibc, iab, div - 1)
drawtri(ic, iac, ibc, div - 1)
drawtri(iab, ibc, iac, div - 1)
# Create vertices
for i in range(20):
drawtri(int(tindices[i][0]), int(tindices[i][1]), int(tindices[i][2]),
ndiv)
# Create normals and scale vertices
normals = vertices.copy()
vertices *= radius
# Create faces
faces = np.array(faces, dtype='uint32')
# Done
return vertices, faces, normals
def getSphere(ndiv=3, radius=1.0):
# Example taken from the Red book, end of chaper 2.
# Define constants
X = 0.525731112119133606
Z = 0.850650808352039932
# Creta vdata
vdata = Pointset(3)
app = vdata.append
app(-X, 0.0, Z)
app(X, 0.0, Z)
app(-X, 0.0, -Z)
app(X, 0.0, -Z)
app(0.0, Z, X)
app(0.0, Z, -X)
app(0.0, -Z, X)
app(0.0, -Z, -X)
app(Z, X, 0.0)
app(-Z, X, 0.0)
app(Z, -X, 0.0)
app(-Z, -X, 0.0)
# Create faces
tindices = [[0, 4, 1], [0, 9, 4], [9, 5, 4], [4, 5, 8], [4, 8, 1],
[8, 10, 1], [8, 3, 10], [5, 3, 8], [5, 2, 3], [2, 7, 3],
[7, 10, 3], [7, 6, 10], [7, 11, 6], [11, 0, 6], [0, 1, 6],
[6, 1, 10], [9, 0, 11], [9, 11, 2], [9, 2, 5], [7, 2, 11]]
tindices = np.array(tindices, dtype=np.uint32)
# Init vertex array
vertices = Pointset(3)
# Define function to recursively create vertices and normals
def drawtri(a, b, c, div):
if (div <= 0):
vertices.append(a)
vertices.append(b)
vertices.append(c)
else:
ab = Point(0, 0, 0)
ac = Point(0, 0, 0)
bc = Point(0, 0, 0)
for i in range(3):
ab[i] = (a[i] + b[i]) / 2.0
ac[i] = (a[i] + c[i]) / 2.0
bc[i] = (b[i] + c[i]) / 2.0
ab = ab.normalize()
ac = ac.normalize()
bc = bc.normalize()
drawtri(a, ab, ac, div - 1)
drawtri(b, bc, ab, div - 1)
drawtri(c, ac, bc, div - 1)
drawtri(ab, bc, ac, div - 1)
# Create vertices
for i in range(20):
drawtri(vdata[int(tindices[i][0])], vdata[int(tindices[i][1])],
vdata[int(tindices[i][2])], ndiv)
# Create normals and scale vertices
normals = vertices.copy()
vertices *= radius
# Done
return vertices, normals
def getSphereWithFaces(ndiv=3, radius=1.0):
# Example taken from the Red book, end of chaper 2.
# Define constants
X = 0.525731112119133606
Z = 0.850650808352039932
# Creta vdata
vdata = Pointset(3)
app = vdata.append
app(-X, 0.0, Z); app(X, 0.0, Z); app(-X, 0.0, -Z); app(X, 0.0, -Z)
app(0.0, Z, X); app(0.0, Z, -X); app(0.0, -Z, X); app(0.0, -Z, -X)
app(Z, X, 0.0); app(-Z, X, 0.0); app(Z, -X, 0.0); app(-Z, -X, 0.0)
# Create faces
tindices = [
[0,4,1], [0,9,4], [9,5,4], [4,5,8], [4,8,1],
[8,10,1], [8,3,10], [5,3,8], [5,2,3], [2,7,3],
[7,10,3], [7,6,10], [7,11,6], [11,0,6], [0,1,6],
[6,1,10], [9,0,11], [9,11,2], [9,2,5], [7,2,11] ]
tindices = np.array(tindices, dtype=np.uint32)
# Init vertex array with existing points, init faces as empty list
vertices = vdata.copy()
faces = []
# Define function to recursively create vertices and normals
def drawtri(ia, ib, ic, div):
a, b, c = vertices[ia] , vertices[ib], vertices[ic]
if (div<=0):
# Store faces here
faces.extend([ia, ib, ic])
else:
# Create new points
ab = Point(0,0,0)
ac = Point(0,0,0)
bc = Point(0,0,0)
for i in range(3):
ab[i]=(a[i]+b[i])/2.0;
ac[i]=(a[i]+c[i])/2.0;
bc[i]=(b[i]+c[i])/2.0;
ab = ab.normalize(); ac = ac.normalize(); bc = bc.normalize()
# Add new points
i_offset = len(vertices)
vertices.append(ab)
vertices.append(ac)
vertices.append(bc)
iab, iac, ibc = i_offset+0, i_offset+1, i_offset+2
#
drawtri(ia, iab, iac, div-1)
drawtri(ib, ibc, iab, div-1)
drawtri(ic, iac, ibc, div-1)
drawtri(iab, ibc, iac, div-1)
# Create vertices
for i in range(20):
drawtri( int(tindices[i][0]),
int(tindices[i][1]),
int(tindices[i][2]),
ndiv )
# Create normals and scale vertices
normals = vertices.copy()
vertices *= radius
# Create faces
faces = np.array(faces, dtype='uint32')
# Done
return vertices, faces, normals