def chain_compose_after_inplace_chain_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
t = Translation([3, 4])
s = Scale([4, 2])
chain_1 = TransformChain([t, s])
chain_2 = TransformChain([s.pseudoinverse(), t.pseudoinverse()])
chain_1.compose_before_inplace(chain_2)
points = PointCloud(np.random.random([10, 2]))
chain_res = chain_1.apply(points)
assert(np.allclose(points.points, chain_res.points))
def model_to_clip_transform(points, xy_scale=0.9, z_scale=0.3):
r"""
Produces an Affine Transform which centres and scales 3D points to fit
into the OpenGL clipping space ([-1, 1], [-1, 1], [1, 1-]). This can be
used to construct an appropriate projection matrix for use in an
orthographic Rasterizer. Note that the z-axis is flipped as is default in
OpenGL - as a result this transform converts the right handed coordinate
input into a left hand one.
Parameters
----------
points: :map:`PointCloud`
The points that should be adjusted.
xy_scale: `float` 0-1, optional
Amount by which the boundary is relaxed so the points are not
right against the edge. A value of 1 means the extremities of the
point cloud will be mapped onto [-1, 1] [-1, 1] exactly (no boarder)
A value of 0.5 means the points will be mapped into the range
[-0.5, 0.5].
Default: 0.9 (map to [-0.9, 0.9])
z_scale: float 0-1, optional
Scale factor by which the z-dimension is squeezed. A value of 1
means the z-range of the points will be mapped to exactly fit in
[1, -1]. A scale of 0.1 means the z-range is compressed to fit in the
range [0.1, -0.1].
Returns
-------
:map:`Affine`
The affine transform that creates this mapping
"""
# 1. Centre the points on the origin
center = Translation(points.centre_of_bounds()).pseudoinverse()
# 2. Scale the points to exactly fit the boundaries
scale = Scale(points.range() / 2.0)
# 3. Apply the relaxations requested - note the flip in the z axis!!
# This is because OpenGL by default evaluates depth as bigger number ==
# further away. Thus not only do we need to get to clip space [-1, 1] in
# all dims) but we must invert the z axis so depth buffering is correctly
# applied.
b_scale = NonUniformScale([xy_scale, xy_scale, -z_scale])
return center.compose_before(scale.pseudoinverse()).compose_before(b_scale)
def model_to_clip_transform(points, xy_scale=0.9, z_scale=0.3):
r"""
Produces an Affine Transform which centres and scales 3D points to fit
into the OpenGL clipping space ([-1, 1], [-1, 1], [1, 1-]). This can be
used to construct an appropriate projection matrix for use in an
orthographic Rasterizer. Note that the z-axis is flipped as is default in
OpenGL - as a result this transform converts the right handed coordinate
input into a left hand one.
Parameters
----------
points: :map:`PointCloud`
The points that should be adjusted.
xy_scale: `float` 0-1, optional
Amount by which the boundary is relaxed so the points are not
right against the edge. A value of 1 means the extremities of the
point cloud will be mapped onto [-1, 1] [-1, 1] exactly (no boarder)
A value of 0.5 means the points will be mapped into the range
[-0.5, 0.5].
Default: 0.9 (map to [-0.9, 0.9])
z_scale: float 0-1, optional
Scale factor by which the z-dimension is squeezed. A value of 1
means the z-range of the points will be mapped to exactly fit in
[1, -1]. A scale of 0.1 means the z-range is compressed to fit in the
range [0.1, -0.1].
Returns
-------
:map:`Affine`
The affine transform that creates this mapping
"""
# 1. Centre the points on the origin
center = Translation(points.centre_of_bounds()).pseudoinverse()
# 2. Scale the points to exactly fit the boundaries
scale = Scale(points.range() / 2.0)
# 3. Apply the relaxations requested - note the flip in the z axis!!
# This is because OpenGL by default evaluates depth as bigger number ==
# further away. Thus not only do we need to get to clip space [-1, 1] in
# all dims) but we must invert the z axis so depth buffering is correctly
# applied.
b_scale = NonUniformScale([xy_scale, xy_scale, -z_scale])
return center.compose_before(scale.pseudoinverse()).compose_before(b_scale)
