Visualizing Spheres

See also

Visualizing ddg objects in Blender for a general guide on visualization of ddg objects in Blender and usage of to_blender_object() and to_blender_object_helper().

Circles and 2D spheres in Euclidean 3D space can be visualized in Blender. For this, a SphereLike needs to be converted to a SmoothNet (SmoothCurve). This has to be converted to a DiscreteNet (or a DiscreteCurve), which is achieved by sampling. This conversion and sampling can be done manually and the DiscreteNet can be handed to to_blender_object(). Alternatively, SphereLike can be handed to to_blender_object_helper() which combines the conversion, the sampling and the call of to_blender_object().

Note

Another possible way to visualize a 2d sphere is to convert it to an icosphere, which is a halfedge surface. This can be done using the function to_halfedge(). The icosphere can then be visualized in Blender using to_blender_object(), see also Visualizing halfedge objects in Blender. This conversion is not (yet) part of this guide, the internal conversion in to_blender_object_helper() is via SmoothNet and DiscreteNet.

Using to_blender_object

A Sphere can be converted to a SmoothNet that can be sampled to a DiscreteNet. The function sample_smooth_net requires a sampling.

>>> import ddg
>>> import numpy as np

>>> euc3d = ddg.geometry.euclidean(3)
>>> sphere = euc3d.sphere(np.array([3.0, 0.0, 1.0, 1.0]), 1.0)
>>> snet = ddg.to_smooth_net(sphere)
>>> dnet = ddg.sample_smooth_net(snet, sampling=[0.5, 10, "c"])

See also

Guide on sampling a SmoothNet.

The DiscreteNet can be visualized:

>>> blender_object = ddg.to_blender_object(dnet)

General arguments of the function to_blender_object() can be found in its api documentation: to_blender_object().

There are additional arguments for the DiscreteNets depending on the dimension of the Sphere:

Options for DiscreteNet:

boundingint (default=10)

Used to bound unbounded domains of nets.

only_wirebool (default=False)

When True, only the wireframe of the net will be created.

Options for DiscreteCurve:

boundingint (default=10)

Used to bound unbounded domains of nets.

curve_typestring (default=’POLY’)

Blender curve type. See the Blender docs for all available types.

curve_propertiesdictionary (default={‘bevel_depth’: 0.015})

Dictionary containing Blender curve properties. See the Blender docs for all available properties.

Options for PointNet:

sphere_radiusfloat (default=0)

Radius of the sphere representing a point.

sphere_subdivisionint (default=3)

How many subdivisions will be applied to the sphere.

See also

Usage of to_blender_object.

Using to_blender_object_helper

The function to_blender_object_helper() combines the following

• easy handling of commonly used keyword arguments

• conversion to objects that can be visualized

• calling the function to_blender_object().

A Sphere can be handed directly to to_blender_object_helper() together with a sampling.

>>> subspace = ddg.geometry.subspaces.subspace_from_affine_points(
...     (0, 0, 0), (1, 0, 0), (0, 1, 0)
... )
>>> blender_object = ddg.to_blender_object_helper(subspace, sampling=[0.5, 10, "c"])

General arguments of the function to_blender_object_helper() can be found in its api documentation: to_blender_object_helper().

There are additional arguments for the (converted) Nets depending on the dimension of the Sphere:

Options for SmoothNet:

samplinglist, int or float

See ddg.datastructures.nets.conversion.sample_smooth_domain().

anchorlist or None

Anchor point for sampling process.

atollist, int or float

Tolerance(s) for sampling process.

Options for DiscreteNet:

boundingint (default=10)

Used to bound unbounded domains of nets.

only_wirebool (default=False)

When True, only the wireframe of the net will be created.

Options for DiscreteCurve:

boundingint (default=10)

Used to bound unbounded domains of nets.

curve_typestring (default=’POLY’)

Blender curve type. See the Blender docs for all available types.

curve_propertiesdictionary (default={‘bevel_depth’: 0.015})

Dictionary containing Blender curve properties. See the Blender docs for all available properties.

Options for PointNet:

sphere_radiusfloat (default=0)

Radius of the sphere representing a point.

sphere_subdivisionint (default=3)

How many subdivisions will be applied to the sphere.

See also

Usage of to_blender_object_helper.

Examples

An example script of creating a circle and visualizing it in Blender:

>>> P1 = np.array([12.0, 0.0, 1.0, 1.0])
>>> P2 = np.array([0.0, 9.0, 1.0, 1.0])
>>> P3 = np.array([1.0, 5.0, 4.0, 7.0])
>>> center = P1 - P3
>>> euc3d = ddg.geometry.euclidean(3)
>>> circle = euc3d.sphere(center, 1.0, subspace=[P1, P2, P3])
>>> snet = ddg.to_smooth_net(circle)
>>> dnet = ddg.sample_smooth_net(snet, sampling=[0.5, 10, "c"])
>>> ddg.to_blender_object_helper(dnet)
bpy.data.objects['SmoothCurve']

Two example renderings:

A render of Ford circles using smooth nets.

A wireframe render of an icosphere (a Sphere converted to a halfedge object).