Procedural Geometry Jaanus Jaggo 1 Procedural geometry uses - - PowerPoint PPT Presentation

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Procedural Geometry Jaanus Jaggo 1 Procedural geometry uses - - PowerPoint PPT Presentation

Jun 05, 2023 22 likes •474 views

Procedural Geometry Jaanus Jaggo 1 Procedural geometry uses Sprite fonts 2D sprites geometrization Procedural landscapes Procedural flora Procedural destruction Meshing point clouds Procedural growth 2

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Procedural Geometry

Jaanus Jaggo

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Procedural geometry uses

  • Sprite fonts
  • 2D sprites geometrization
  • Procedural landscapes
  • Procedural flora
  • Procedural destruction
  • Meshing point clouds
  • Procedural growth

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Pandora from Avatar movie - uses a lot of procedural geometry

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Sprite Fonts

Blizzard’s TCG card

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Sprite fonts generation

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2D sprite geometrization

  • GPU can handle loads of vertices
  • limited in Pixel Fill-Rate

67% of pixels saved

Source: http://discuss.cocos2d-x.org/t/new-feature-meshsprite-polygonsprite-updated/21153

Performance: (number of sprites rendered within 40 FPS)

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2D sprite geometrization

Unity does it automatically Can we do better?

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How it’s done proceduraly?

https://unity3d.com/learn/resources/boosting-graphics-performance-2d-games Algorithm by Erik Grahm

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Edge detection

substracted

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Edge detection

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Find closed path around the object

Problems: loops and deadlocks

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Simplify the polygon

Convex hull algorithm

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Simplify the polygon

Convex hull algorithm

kick out points that produce triangles

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Triangulation

Computational Geometry (Springer, third edition, 2008) This algorithm can triangulate polygons with holes

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Triangulation complexity

  • Ear clipping method - O(n2)
  • Using monotone polygons O(n log n)
  • Can be done within O(n) <- some complicated algorithms

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UV’s

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Optimizing it further

2-layered approach 2 layers == 2 draw calls

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Procedural landscape

  • Height field terrain
  • Vector field terrain
  • Voxel based terrain

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Heightmap based landscapes

  • Main game engines -> built in

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Halo Wars: The Terrain Of Next Gen - (vector field terrain) http://www.gdcvault. com/play/1277/HALO-WARS-The-Terrain-of

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Height field vs. Vector field

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Voxel based procedural landscapes

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Smooth Voxels

http://nerdkingdomofficial.tumblr.com/post/119558446658/dev-blog-44-voxelize-this

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Isosurface extraction

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  • Marching cubes
  • Marching Tetrahedra
  • Surface nets
  • Dual contouring

Demo: http://mikolalysenko.github. io/Isosurface/ http://http.developer.nvidia.com/GPUGems3/gpugems3_ch01.html

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Marching cubes

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28 = 256 different possibilities Problem: some cases are ambigious

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Marching cubes

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Marching Tetrahedra

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Solves ambigiouty problem 24 = 16 different possibilities Problem: may produce artificial “bumps”

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Surface nets

Minecraft ;)

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Comparison

  • Marching cubes

○ + pretty fast ○ + most widely known

  • Marching tetrahedra

○ + solves ambigouty problem ○

  • much slower

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  • far larger meshes
  • Surface nets

○ + fast ○ + slightly smaller meshes than first two ○

  • non-manifold vertices

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http://0fps.net/2012/07/12/smooth-voxel-terrain-part-2/ non-manifold vertices

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Procedural flora

  • L-systems
  • Superformula

No man sky

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L-systems

Formal method for describing self similar objects.

http://buildingindustry.org/l-systems

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Superformula

Mathematical formula used to describe many complex shapes in nature.

parameters: a = b = 1 m, n1, n2, n3

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Procedural destruction

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Assets in Unity assets store

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Shattering glass

before: https://www.youtube.com/watch?v=eQXCHfmsHQA after: https://www.youtube.com/watch?v=7U6kPGgGe1s

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Shattering glass

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http://cowboyprogramming.com/2007/01/05/shattering-reality/

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Voronoi diagrams

https://www.youtube.com/watch?v=XYs5WOc4Etg http://forum.unity3d.com/threads/fracture-dynamic-destruction-system.177066/

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Partitioning of a plane into regions based on distance to points (any point inside a region is closest to the origin)

Euclidean distance Manhattan distance

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Fortune’s algorithm

Sweep line algorithm for making voronoi diagrams

  • Vertical sweep line moves left to right
  • Beach line is a curve left to sweep line
  • Left of beach line all points are known
  • beach line progresses by keeping each parabola base exactly half way

between points initially swept and the sweep line

  • Beach line is maintained in binary search tree
  • Future points are maintained in priority queue
  • Algorithm repeatedly removes next event from priority queue and updates the

data structure.

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O(n) events & O(log n) time to process an event = O(n log n) time

https://en.wikipedia.org/wiki/Fortune%27s_algorithm

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More uses for voronoi

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More uses for voronoi

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Supernoi (multiple voronoi)

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http://www.daxpandhi.com/post/Stark-Desert-Rocks

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Meshing point clouds

https://www.youtube.com/watch?v=_RHXqG7HlEM

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1. Subsampling a. reducing the dataset 2. Normal reconstruction 3. Surface reconstruction a. marching cube algorithms b. quadric edge collapse simplification 4. Recovering original color 5. Cleaning up and assessing

http://meshlabstuff.blogspot.com.ee/2009/09/meshing-point-clouds.html There are also other methods for example Voronoi filtering for steps 2 and 3

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Procedural growth

https://www.youtube.com/watch?v=9HI8FerKr6Q

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https://vimeo.com/27913396

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Growing citys

A roadmap generated:

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https://josauder.github.io/procedural_city_generation/

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Growing citys

Rules:

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Growing rules

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Rule Forward Turn pForward pTurn grid

vert + prev_vec

vert + rot 90

1 0.09

  • rganic

vert + random rot vert + rot (60,120)

1 0.8 radial

vert + adjust vec vert + adjust vec

1 0.07 minor road

vert + prev_vec vert + rot 90

0.05 0.85

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Vertex snapping

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Thank you for listening

Here is a kitten for you!

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