Homeomorphic meshes

Homeomorphic meshes

Morphing between meshes using GLSL

The construction of space point and line to plane point to plane algorithmic construction of space the isomorphic relationality between

This project sets out to explore the methods which can be used to construct triangles from points. The aim is to avoid the standard algorithmic procedures; the Delaunay or the Voronoi, in line with the algorists. http://rhizome.org/editorial/2012/jul/5/prosthetic-knowledge-picks-algorists/

A bug results in triangles which do not map to the surface connecting the points

The 3D point clouds of two plants were created using a Kinect, the vertices were ordered to create two homemorphic collections of points in the same space.

The image from a Kinect camera is used to sample the depth of points in space to create a three dimensional point cloud

An algorithmic construction of reality

Point to line and plane an algorithm can be used to create a real space, the simulation could be further reified by 3D printing. A snapshot of a movement of points through space. Multiple snapshots cannot reconstruct the fluidity of time, here Duchamp fails.

Always in the middle never one nor the other but always at the same time a proportion of the sum of the one and the other.

A snap shot of the screen whilst animating between two 3D meshes, the resulting form seems to retain the plants' colours and structures

A process takes each point of the first mesh and finds all points within the nearest 20 units of space. The whole thing is 5000 units so 16cm might be a good assumption. Real space is mapped into data and processed in the following way:

for each point
    - find the nearest 20 points in the mesh within a set radius
    - find the range and average value of the green component of the colour at that point
    - insert into the mesh a random number of triangles relative to quantity of green the point

This process can be repeated at various scales connecting points on degrees of locaility in real space resulting in a layering of triangles.

Sometimes bugs construct distorted spaces.

A bug causes a strange and distored space to appear, stangely appealling in broken and false places distributed through space

Animating space

Order by location so the that the two set of vertex positions are ordered by the spatial proximity. For the spaces to be homeomorphic they must be identical in the number of points.

The resulting code animates a partial interpolated space between two static forms never settling in either. The interpolation combines a sin waveform with Perlin noise to force a fibrillating movement between positions.