Shape Interpolation

Given two shapes as triangulated 3D models, how can we smoothly interpolate another model between them using signed distance fields

import numpy as np
import pyvista as pv

import mirage as mr

Animating the entire interpolation

obj1 = mr.SpaceObject('icosahedron.obj').clean()
obj2 = mr.SpaceObject('duck.obj').clean()

pl = pv.Plotter()
pl.open_gif('shape_interpolation.gif')

for frac1 in np.concatenate((np.linspace(0, 1, 20), np.linspace(1, 0, 20))):
    weights = np.array([1 - frac1, frac1]).astype(float)
    mr.tic()
    obj_merged = mr.merge_shapes([obj1, obj2], weights)
    mr.toc()
    pl.add_mesh(obj_merged._mesh, color='lightblue', name='mesh', smooth_shading=True)
    pl.add_text(
        f'{weights[0] * 100:3.0f}% Icosahedron \n{weights[1] * 100:3.0f}% Duck',
        font='courier',
        name='label',
    )
    pl.write_frame()
pl.close()

Model file duck.obj not found in current model folder ('/Users/liamrobinson/Documents/maintained-research/mirage/mirage/resources/models'), checking model repository...
Attempting to download duck.obj and its associated material file from the model repository...
Requesting: https://raw.githubusercontent.com/ljrobins/mirage-models/main//Non-Convex/duck.obj
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Individual interpolation steps in a grid

pl = pv.Plotter(shape=(2, 2))

for i, weight1 in enumerate(np.linspace(0, 1, 4)):
    weights = np.array([1 - weight1, weight1]).astype(float)
    obj_merged = mr.merge_shapes(
        [
            mr.SpaceObject('icosahedron.obj').clean(),
            mr.SpaceObject('torus.obj').clean(),
        ],
        weights,
    )
    pl.subplot(i // 2, i % 2)
    pl.add_mesh(obj_merged._mesh, color='lightblue', name='mesh', smooth_shading=True)
    pl.add_text(
        f'{weights[0] * 100:3.0f}% Icosahedron \n{weights[1] * 100:3.0f}% Torus',
        font='courier',
        name='label',
    )
pl.show()

Model file torus.obj not found in current model folder ('/Users/liamrobinson/Documents/maintained-research/mirage/mirage/resources/models'), checking model repository...
Attempting to download torus.obj and its associated material file from the model repository...
Requesting: https://raw.githubusercontent.com/ljrobins/mirage-models/main//Non-Convex/torus.obj
Requesting: https://raw.githubusercontent.com/ljrobins/mirage-models/main//Non-Convex/torus.mtl
Model files were downloaded successfully!