The code below takes the SVG file on the left and does a nice job of
transforming it into the hemisphere on the right.
I’ve looked at shrinkwrap and lattice, via the link below:
Lattice & Shrinkwrap modifier - Blender Tutorial
which provides some insights as to how it might be done.
Say for example, I take a polyhedral shape or a geodesic dome,
cut it in half and try to accomplish the same thing as above).
Would there be a way to do that NOT using python? The code
is intended for a hemisphere. I’d like to expand (if possible) my
options and possibilities.
Thanx
The Python code:
"""
A script to create stereographic lampshades from SVG patterns
Inspired by http://jasmcole.com/2014/11/01/stereographic-lampshades/
"""
import bpy
from math import cos, sin, atan, atan2
def convert_to_polar_coordinates(x, y):
"""
finds the polar coordinates given cartesian x and y
returns r, theta(degrees)
"""
polar_radius = (x ** 2 + y ** 2) ** .5
polar_phi = atan2(y,x)
return polar_radius, polar_phi
def compute_angle_from_top_lampshade(r, a, h):
return atan(float(r) / (a + h))
def compute_new_coordinates(vertex_coordinates, distance_to_center_of_lampshade, radius_of_lampshade):
"""
Back computing the projection onto the sphere
"""
x, y, z = vertex_coordinates
polar_radius, polar_phi = convert_to_polar_coordinates(x,y)
theta = compute_angle_from_top_lampshade(
polar_radius,
radius_of_lampshade,
distance_to_center_of_lampshade
)
alpha = 2 * theta
x_new = radius_of_lampshade * sin(alpha) * cos(polar_phi)
y_new = radius_of_lampshade * sin(alpha) * sin(polar_phi)
z_new = distance_to_center_of_lampshade - radius_of_lampshade * cos(alpha)
return (x_new, y_new, z_new)
def move_svg_to_origin():
"""
Moves the SVG Object to origin
"""
bpy.ops.object.mode_set(mode="OBJECT")
#move the object to origin
bpy.ops.object.origin_set(type="GEOMETRY_ORIGIN")
def scale_svg(factor):
#only scale x and y because SVG a flat image
bpy.ops.transform.resize(
value=(factor,factor, 1.0)
)
#need to transform apply otherwise the resize won't affect the mesh coordinates
bpy.ops.object.transform_apply(
location=False,
rotation=False,
scale=True
)
def setup_svg(scale=100):
"""
Assume the imported SVG is very small, scale the SVG up for easier manipulation
"""
move_svg_to_origin()
scale_svg(scale)
def convert_svg_to_mesh():
#convert SVG (Blender Curve) to a Mesh
bpy.ops.object.convert(target='MESH', keep_original=False)
cleanup_mesh_to_reduce_future_artifacts()
def rearrange_faces_for_better_results():
"""
This will remove long thin faces, that will cause artifacts
"""
bpy.ops.object.mode_set(mode="EDIT")
bpy.ops.mesh.select_all(action="SELECT")
bpy.ops.mesh.beautify_fill()
bpy.ops.object.mode_set(mode="OBJECT")
def change_mesh_color_for_better_visualization(selected_object):
#fancy display to better visualize the changes
selected_object.data.materials[0].diffuse_color = (1.0, 1.0, 1.0)
def remove_duplicate_vertices():
bpy.ops.object.mode_set(mode="EDIT")
bpy.ops.mesh.select_all(action="SELECT")
bpy.ops.mesh.remove_doubles(use_unselected=True)
#need to switch modes for the remove doubles to apply
bpy.ops.object.mode_set(mode="OBJECT")
def make_normals_consistently_outwards():
bpy.ops.object.mode_set(mode="EDIT")
bpy.ops.mesh.select_all(action="SELECT")
bpy.ops.mesh.normals_make_consistent()
bpy.ops.object.mode_set(mode="OBJECT")
def extrude(value):
bpy.ops.object.mode_set(mode="EDIT")
bpy.ops.mesh.extrude_region_move(
TRANSFORM_OT_translate={"value":(0,0,value)}
)
def scale_after_extrusion(extrude_value, radius_of_lampshade):
"""
Proportionally scale outwards after the extrusion to create a lampshade with some thickness
"""
resize = 1 - extrude_value/radius_of_lampshade
bpy.ops.transform.resize(value=(resize, resize, resize))
def cleanup_mesh_to_reduce_future_artifacts():
remove_duplicate_vertices()
rearrange_faces_for_better_results()
def transform_to_lampshade(selected_object, distance_to_center_of_lampshade, radius_of_lampshade):
for vertex in selected_object.data.vertices:
vertex.co = compute_new_coordinates(vertex.co, distance_to_center_of_lampshade, radius_of_lampshade)
def make_printable(thickness, radius_of_lampshade):
make_solid(thickness, radius_of_lampshade)
make_normals_consistently_outwards()
def make_solid(thickness, radius_of_lampshade):
extrude(thickness)
scale_after_extrusion(thickness, radius_of_lampshade)
def create_stereographic_lampshade(distance_to_center_of_lampshade,
radius_of_lampshade,
thickness_of_lampshade):
"""
distance_to_center_of_lampshade and radius_of_lampshade are used to back project the SVG
the actual height and radius may very a little depending on the thickness_of_lampshade
"""
selected_object = bpy.context.scene.objects.active
setup_svg()
convert_svg_to_mesh()
change_mesh_color_for_better_visualization(selected_object)
transform_to_lampshade(selected_object, distance_to_center_of_lampshade, radius_of_lampshade)
make_printable(thickness_of_lampshade, radius_of_lampshade)
create_stereographic_lampshade(
distance_to_center_of_lampshade=5,
radius_of_lampshade=5,
thickness_of_lampshade=0.15)
