The Blender hypermesh addon allows the manipulation of meshes in 4-dimensional Euclidean space. This is achieved by using ordinary Blender tools to manipulate projections of this 4-mesh to 3-dimensional Euclidean space.
This document described the internal workings of the hypermesh addon. It is not intended for end users, but as a document to help in understanding the code.
When the hypermesh plugin is loaded, the following extra information is kept track of:
HyperSettings object, which keeps track of
When a mesh is turned into a hypermesh (by the MakeHyperOperator),
or when a hypermesh is inserted directly,
the Bmesh data underlying it contains 4 extra layers of floating point vertex information.
These layers are called hyperw, hyperx, hypery, hyperz, and they contain the
coordinates of the vertex in 4-space.
Of course, the ordinary 3-coordinates are related to these 4 hypercoordinates by means of the projection used. To ensure that this relation is maintained at all times, the following actions have to be undertaken:
It should be noted that this is not what the addon does.
For performance reasons, it doesn’t update the 4-coordinates automatically
whenever the 3-coordinates change. Rather, it marks the 4-coordinates as needing
an update by setting the mesh’s hypermesh-dirty property to True.
Then whenever the 4-coordinates are needed (for example, when the 3-coordinates need to be
updated based on their value, or when they need to be shown in the UI),
they are updated (and hypermesh-dirty is set to False).
These are the essential workings of the addon.
The starting point of the plugin. It does the following things:
bl_info, which is read by Blender to provide information about the plugin,scene_update_post; this is used to detect when a
mesh has been edited<shift+a>)When a mesh has been edited in such a way that its 4-coordinates are no longer valid,
the mesh’s hypermesh-dirty property should be set to True. This is done in this file.
When a mesh’s hypercoordinates are recalculated from the coordinates in 3-space,
this will trigger the scene_update_post event, which in turn will mark the coordinates as
dirty (even though they’re not). To prevent this, a property hypermesh-justcleaned is used
to indicate that the handler for scene_update_post should not mark this mesh as dirty
the next time it is invoked.
Operator that inserts a flat torus into the scene.
The UI panel that is visible when editing a mesh (edit mode in the 3D view).
Defines the user preferences that available for this addon. Only one is available: whether or not to enable debugging. If debugging is enabled, the addon will print debug messages to the system console.
A HyperPreset is a PropertyGroup that contains the information defining a projection from 4-space
to 3-space.
(It’s a list of these that the scene keeps track of.)
It also contains code that handles projection changes (by updating all meshes that use this projection).
Finally, it contains code that defines several standard projections from 4-space to 3-space.
These are projections that are probably useful in manipulating 4-meshes.
Panel that is shown when a mesh is selected to pick which projection to use. Selecting a projection here sets the selected object’s projection.
Panel that is shown in the scene’s properties listing all the projections that exist in the scene. Allows editing of projections.
A HyperSettings object is a PropertyGroup that is associated to each mesh,
indicating whether the mesh is a hypermesh, and which projection is in use.
Also contains code to update a mesh when a different projection is picked.
Operator that inserts a hypercube into the scene.
Operator that turns an existing mesh into a hypermesh.
This file contains the mathematical transformations relating 3-space to 4-space.
Operator that updates the 4-dimensional positions of a mesh’s vertices on demand. Useful if you want to programmatically access hypercoordinates that haven’t been recalculated yet.
If you are not accessing the hypercoordinates programmatically, it should never be necessary
to call the Update hypercoordinates operator.
Any behavior that is observable from the UI should be indistinguishable from the case where hypercoordinates
are immediately recalculated.
Behavior that does not satisfy this requirement is considered incorrect. Please file a bug report.
The addon stores several pieces of data when in use (hypercoordinates, presets, …). The following provides an overview of all these pieces of data.
The following pieces of information are stored for meshes:
HyperSettings object (called me.hypersettings where me is the mesh)hyperw, hyperx,
hypery, hyperz); these can be accessed from the mesh’s Bmesh datame["hypermesh-dirty"] and me["hypermesh-justcleaned"]
for keeping track of whether hypercoordinates need to be updated (where me is the mesh)About storage in the .blend:
as far as I can tell, no HyperSettings object is written to the .blend unless
it is set at some point in time. For non-hyper-meshes, the HyperSettings are never written
to (they stay at the default), so I don’t think that these meshes take up extra space in the
.blend when the addon is enabled.
The following pieces of information are stored for scenes:
HyperPresets (called sc.hyperpresets where sc is the scene)IntProperty called sc.selectedpreset; it indicates which preset is currently
selected in the scene’s properties; this property is not written to the .blendThe convention in all of Hypermesh’s code is to use the order WXYZ for the coordinates.
This works well, except for one issue: Blender’s class mathutils.Vector disagrees.
Indeed, if v is a mathutils.Vector, then v.w == v[3].
To circumvent this problem,
the coordinates of a mathutils.Vector shall never be indexed using letters
in Hypermesh code.
Incorrect is:
v = Vector([1, 2, 3, 4])
the_w = v.w # this is now 4
Correct is:
v = Vector([1, 2, 3, 4])
the_w = v[0] # this is now 1