From 9db0348acb7ae5911594d3f848c347afa20db60b Mon Sep 17 00:00:00 2001
From: andersct <andersct@umich.edu>
Date: Sat, 24 Oct 2020 20:22:37 -0400
Subject: [PATCH] Add asteroids for space examples
- add display for asteroid
- generate random convex asteroids by sampling normals
- add functions to fix surface triangulations
- add figure setting for space background
---
examples/display_asteroid.py | 50 +++++++++++++++++++++++
examples/display_shuttle_model.py | 7 +++-
rigid_body_models/shuttle.py | 1 +
rigid_body_models/triangulated_surface.py | 39 ++++++++++++++++++
scene_elements_3d/__init__.py | 0
scene_elements_3d/asteroid.py | 45 ++++++++++++++++++++
vis/triangulated_surface.py | 6 ++-
vis/xyz_utils.py | 9 ++++
8 files changed, 154 insertions(+), 3 deletions(-)
create mode 100644 examples/display_asteroid.py
create mode 100644 scene_elements_3d/__init__.py
create mode 100644 scene_elements_3d/asteroid.py
diff --git a/examples/display_asteroid.py b/examples/display_asteroid.py
new file mode 100644
index 0000000..2666f78
--- /dev/null
+++ b/examples/display_asteroid.py
@@ -0,0 +1,50 @@
+import numpy as np
+import plotly.graph_objects as go
+import scene_elements_3d.asteroid as ast
+from vis import triangulated_surface as vtrs
+from vis.xyz_utils import set_space_background
+
+
+def main(is_surface_normals=False):
+ seed = np.random.randint(1000)
+ print('seed: {}'.format(seed))
+ # seed = 0
+ np.random.seed(seed)
+ mu = np.array([
+ [0., 0, 0],
+ [2, 0, 1],
+ ])
+ sigma = np.array([
+ [
+ [2., 0, 0],
+ [0, 1, 0],
+ [0, 0, 1],
+ ],
+ [
+ [1., 0, .2],
+ [0, 1, 0],
+ [.2, 0, 1],
+ ],
+ ])
+ model = ast.generate_convex_asteroid(mu, sigma, 100)
+
+ fig = go.Figure()
+ fig.add_traces([vtrs.make_model_mesh(model)])
+ if is_surface_normals:
+ fig.add_traces(vtrs.make_surface_normals(
+ model.vertices, model.triangles))
+ title_str = 'Asteroid'
+ fig.update_layout(
+ title=title_str, autosize=False,
+ width=1200, height=600,
+ scene=dict(
+ xaxis=dict(range=[-8, 8]),
+ yaxis=dict(range=[-6, 6]),
+ zaxis=dict(range=[-6, 6]),
+ ), showlegend=False)
+ set_space_background(fig)
+ fig.show()
+
+
+if __name__ == '__main__':
+ main(is_surface_normals=False)
diff --git a/examples/display_shuttle_model.py b/examples/display_shuttle_model.py
index 829955e..b4366fe 100644
--- a/examples/display_shuttle_model.py
+++ b/examples/display_shuttle_model.py
@@ -2,9 +2,10 @@ import plotly.graph_objects as go
from rigid_body_models.shuttle import Shuttle
from vis import triangulated_surface as vtrs
from vis import triangulated_thruster_model as vttm
+from vis.xyz_utils import set_space_background
-def main_display_mesh(is_thrusters=True):
+def main_display_mesh(is_thrusters=True, is_space_bg=True):
model = Shuttle(rho=1e6)
fig = go.Figure()
fig.add_traces([vtrs.make_model_mesh(model)])
@@ -23,8 +24,10 @@ def main_display_mesh(is_thrusters=True):
yaxis=dict(range=[-6, 6]),
zaxis=dict(range=[-6, 6]),
), showlegend=is_thrusters)
+ if is_space_bg:
+ set_space_background(fig)
fig.show()
if __name__ == '__main__':
- main_display_mesh(is_thrusters=True)
+ main_display_mesh(is_thrusters=True, is_space_bg=True)
diff --git a/rigid_body_models/shuttle.py b/rigid_body_models/shuttle.py
index 24e8a3b..4a44bbe 100644
--- a/rigid_body_models/shuttle.py
+++ b/rigid_body_models/shuttle.py
@@ -86,3 +86,4 @@ class Shuttle(trs.TriangulatedSurface):
_, _, im = trs.calculate_mass_properties(
self.vertices, self.triangles, rho)
self.im = im
+ self.color = 'white'
diff --git a/rigid_body_models/triangulated_surface.py b/rigid_body_models/triangulated_surface.py
index 3a9a0e7..010089d 100644
--- a/rigid_body_models/triangulated_surface.py
+++ b/rigid_body_models/triangulated_surface.py
@@ -69,3 +69,42 @@ def calculate_mass_properties(vertices, triangles, rho):
[-s[6], -s[5], s[7] + s[8]],
])
return m, center, im
+
+
+def remove_unused_vertices(vertices, triangles):
+ """
+ Remove vertices that do not form a triangle, and relabel triangle vertices
+ to their new indices.
+ :param vertices: n_points, 3 | includes all points forming triangle faces
+ :param triangles: n_faces, 3 | indices of vertices that form each triangle
+ :return: vertices, triangles
+ """
+ used_inds = np.unique(triangles.ravel())
+ vertices_new = vertices[used_inds]
+ triangles_new = triangles.copy()
+ for i in range(used_inds.size):
+ triangles_new[triangles_new == used_inds[i]] = i
+ return vertices_new, triangles_new
+
+
+def make_convex_shape_triangles_consistent(vertices, triangles):
+ """
+ For a convex shape described by a triangulated surface, ensure
+ each triangle's normal faces outward.
+ :param vertices: n_points, 3 | includes all points forming triangle faces
+ :param triangles: n_faces, 3 | indices of vertices that form each triangle
+ :return: triangles: n_faces, 3 | triangles made consistent
+ """
+ used_inds = np.unique(triangles.ravel())
+ center = vertices[used_inds].mean(axis=0)
+ triangle_centers = np.array([
+ vertices[triangles[i]].mean(axis=0) for i in range(len(triangles))
+ ])
+ outward_vec = triangle_centers - center
+ triangle_normals = np.cross(
+ vertices[triangles[:, 1]] - vertices[triangles[:, 0]],
+ vertices[triangles[:, 2]] - vertices[triangles[:, 0]],
+ )
+ is_mismatch = np.einsum('ij,ij->i', outward_vec, triangle_normals) < 0
+ triangles[is_mismatch, :] = triangles[is_mismatch, :][:, [0, 2, 1]]
+ return triangles
diff --git a/scene_elements_3d/__init__.py b/scene_elements_3d/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/scene_elements_3d/asteroid.py b/scene_elements_3d/asteroid.py
new file mode 100644
index 0000000..ed1b98f
--- /dev/null
+++ b/scene_elements_3d/asteroid.py
@@ -0,0 +1,45 @@
+import numpy as np
+from rigid_body_models import triangulated_surface as trs
+from scipy.spatial import ConvexHull
+
+
+def generate_convex_asteroid(mu_list, sigma_list, n_samples_per, **kwargs):
+ """
+ Generate asteroid from the convex hull of samples taken
+ from a list of normals.
+ :param mu_list: n, 3 | means of multivariate normals
+ :param sigma_list: n, 3, 3 | covariance matrix of multivariate normals
+ :param n_samples_per: number of samples per normal
+ :return:
+ vertices:
+ triangles:
+ """
+ samples = []
+ for mu, sigma in zip(mu_list, sigma_list):
+ L = np.linalg.cholesky(sigma)
+ samples_i = (L.dot(np.random.randn(3, n_samples_per))).T + mu
+ samples.append(samples_i)
+ samples = np.vstack(samples) # n*n_samples_per, 3
+ hull = ConvexHull(samples)
+ triangles = hull.simplices
+ vertices = samples
+ vertices, triangles = trs.remove_unused_vertices(vertices, triangles)
+ triangles = trs.make_convex_shape_triangles_consistent(vertices, triangles)
+ asteroid = Asteroid(vertices, triangles, **kwargs)
+ return asteroid
+
+
+class Asteroid(trs.TriangulatedSurface):
+
+ def __init__(self, vertices, triangles, rho=2000.):
+ super(Asteroid, self).__init__(rho, vertices, triangles)
+ m, center, im = trs.calculate_mass_properties(
+ self.vertices, self.triangles, rho)
+ self.m = m
+ self.im = im
+ self.center = 0 * center
+ self.vertices -= center
+ _, _, im = trs.calculate_mass_properties(
+ self.vertices, self.triangles, rho)
+ self.im = im
+ self.color = 'grey'
diff --git a/vis/triangulated_surface.py b/vis/triangulated_surface.py
index 3f48e81..87acdd3 100644
--- a/vis/triangulated_surface.py
+++ b/vis/triangulated_surface.py
@@ -15,10 +15,14 @@ def make_model_mesh(model, Rt=()):
Rt = Rt_3d()
xyz = Rt[:3, :3].dot(model.vertices.T).T + Rt[:3, -1]
ijk = model.triangles
+ try:
+ color = model.color
+ except AttributeError:
+ color = None
mesh = go.Mesh3d(
x=xyz[:, 0], y=xyz[:, 1], z=xyz[:, 2],
i=ijk[:, 0], j=ijk[:, 1], k=ijk[:, 2],
- color='white', flatshading=True
+ color=color, flatshading=True
)
return mesh
diff --git a/vis/xyz_utils.py b/vis/xyz_utils.py
index cdc9b97..dc538ee 100644
--- a/vis/xyz_utils.py
+++ b/vis/xyz_utils.py
@@ -29,3 +29,12 @@ def make_3d_vector(root, vector, scale=1., name=''):
name=name,
)
return line_obj, arrow_head_obj
+
+
+def set_space_background(fig):
+ """
+ :param fig: plotly figure
+ :return:
+ """
+ fig.update_layout(paper_bgcolor='rgb(10,10,10)')
+ fig.update_scenes(xaxis_visible=False, yaxis_visible=False, zaxis_visible=False)
--
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