E1. Geometry

Task:

You have a non-rectangular block in 3D space, which is shown in Pic 1. Now you need to transform the block to the origin and achieve the expected visualization outcome shown in Pic 2. Here are the steps:

1. Find the oriented bounding box of the block,

2. Find the local frame of the bounding box,

3. Transfer the bounding box from its local frame to WorldXY frame,

4. Visualize the xyz-axes of the local frame and WorldXY frame,

5. Use the same Transformation to transform the block

Pic 1: Input block

Pic2: Expected outcome

Code

Ex1.py

import os
from compas.datastructures import Mesh
from compas_view2.app import App

# unserialize the block data
HERE = os.path.dirname(__file__)
FILE = os.path.join(HERE, 'data', 'block.json')
mesh = Mesh.from_json(FILE)

# STEP 1: find the oriented bounding box
# hint1: "points = mesh.vertices_attributes('xyz', keys=mesh.vertices())" 
#        gives you all the points on the block
# hint2: oriented_bounding_box_numpy, Box.from_bounding_box

# STEP 2: find the local frame of the bounding box
# hint: Box.frame

# Step 3: transform the bounding box from local frame to worldXY frame
# hint1: Frame.worldXY, Transformation.from_frame_to_frame, box.transformed(T)
# hint2: add the transformed bounding box to the viewer

# STEP 4: draw the xyz-axes of the local frame, worldXY frame
# hint1: Frame.xaxis, Line, scale_vector
# hint2: add the lines to the viewer

# Step 5: transform the block using the same transformation
# hint1: mesh.transformed(T)
# hint2: add the transformed block to the viewer

# visualization
viewer = App()
viewer.add(mesh)
viewer.run()

Answer

ex1_answer.py

import os
from compas.datastructures import Mesh
from compas.geometry import Box, Line, Transformation, Frame
from compas.geometry import oriented_bounding_box_numpy, scale_vector, add_vectors
from compas_view2.app import App

# unserialize the block data
HERE = os.path.dirname(__file__)
FILE = os.path.join(HERE, 'data', 'block.json')
mesh = Mesh.from_json(FILE)

# STEP 1: find the oriented bounding box
# hint1: "points = mesh.vertices_attributes('xyz', keys=mesh.vertices())" gives you all the points on the block
# hint2: oriented_bounding_box_numpy, Box.from_bounding_box
points = mesh.vertices_attributes('xyz', keys=mesh.vertices())
box = oriented_bounding_box_numpy(points)
box = Box.from_bounding_box(box)

# STEP 2: find the local frame of the bounding box
# hint: Box.frame
local_frame = box.frame

# Step 3: transform the bounding box from local frame to worldXY frame
# hint1: Frame.worldXY, Transformation.from_frame_to_frame, box.transformed(T)
# hint2: add the transformed bounding box to the viewer
world_frame = Frame.worldXY()
T = Transformation.from_frame_to_frame(local_frame, world_frame)
box_T = box.transformed(T)

# STEP 4: draw the xyz-axes of the local frame, worldXY frame
# hint1: Frame.xaxis, Line, scale_vector
# hint2: add the lines to the viewer
local_xaxis = scale_vector(local_frame.xaxis, box.xsize)
local_xline = Line(local_frame.point, add_vectors(
    local_frame.point, local_xaxis))
local_yaxis = scale_vector(local_frame.yaxis, box.ysize)
local_yline = Line(local_frame.point, add_vectors(
    local_frame.point, local_yaxis))
local_zaxis = scale_vector(local_frame.zaxis, box.zsize)
local_zline = Line(local_frame.point, add_vectors(
    local_frame.point, local_zaxis))

world_xline = local_xline.transformed(T)
world_yline = local_yline.transformed(T)
world_zline = local_zline.transformed(T)

# Step 5: transform the block using the same transformation
# hint1: mesh.transformed(T)
# hint2: add the transformed block to the viewer
mesh_T = mesh.transformed(T)

# visualization
viewer = App()
viewer.add(mesh)
viewer.add(box, show_faces=False, show_edges=True)
viewer.add(local_xline, linewidth=3, linecolor=(0, 1, 0))
viewer.add(local_yline, linewidth=3, linecolor=(0, 0, 1))
viewer.add(local_zline, linewidth=3, linecolor=(1, 0, 0))

viewer.add(mesh_T)
viewer.add(box_T, show_faces=False, show_edges=True)
viewer.add(world_xline, linewidth=3, linecolor=(0, 1, 0))
viewer.add(world_yline, linewidth=3, linecolor=(0, 0, 1))
viewer.add(world_zline, linewidth=3, linecolor=(1, 0, 0))

viewer.run()