Attempt to solve the problem of exploring all possible build-able shapes from a given set of various triangles.

**Defining **

**the joint**: a point in 3D space
**joint matrix**: a list of all joints in the scene
**shape matrix**: a matrix of boolean values with columns and rows equal to the total number of joints, storing a true value where two joints are connected and false otherwise.
**craft elements**: a joint matrix and a shape matrix describing sizes from real objects scans

Joint Matrix:

- x, y, z
- 1, 1.4, 1.2
- 1.2, 1.1, 1.9
- 1.4, 1.6, 1.1
- …

Shape Matrix:

1 2 3 4 5 …

- F F T F F
- T F F F F
- F F F T F
- F F T F T
- T F F T F
- …

**Approaches**

**Potential use of Unity Engine’s triangulation of shapes for solving the way triangles can define any 3D shape. (Delaunay Triangulation could be implemented for more control over distribution.)**

Applications:

- Creating the structure of real objects using real object 3D scans (available at this point only on Apple ARKit, announced on Niantic and requested on Google ARCore)
- Recreation of abstract objects with a minimal use of mathematics, relying on Unity’s Engine 3D calculations.

**Breakdown of shapes and implementing of algorithms to solve the spatial placement of the joints and triangles, potentially linking to machine learning. **

Algorithm Candidates

- Backtracking (will be slowest but given small amount of data to process could turn out to be practical)
- Brench and bound (at first glance seems as a potential solution)
- Graph algorithms if the shape is reinterpreted to fit the algorithm.

Applications

- limitless freedom in the shape, here we have individual control over triangles and further more squared or and n-polygon shape that acts as main construction element.
- AI can truly propose the most efficient models that can be computer calculated because of it having access as well to every element in the shape.
- Remixing shapes while keeping them realistic.

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