Texture mapping World/object coordinates 2D/3D Sources : scanners, - - PowerPoint PPT Presentation

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texture mapping world object coordinates 2d 3d sources
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Texture mapping World/object coordinates 2D/3D Sources : scanners, - - PowerPoint PPT Presentation

Apr 05, 2023 95 likes •957 views

Texture mapping World/object coordinates 2D/3D Sources : scanners, raytracers Mapping one object pixel to a texture pixel Object parameterization Planar map shape Planar map shape Planar map shape Cylindrical map shape Cylindrical map

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Texture mapping

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World/object coordinates

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2D/3D

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Sources : scanners, raytracers

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Mapping one object pixel to a texture pixel

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Object parameterization

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Planar map shape

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Planar map shape

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Planar map shape

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Cylindrical map shape

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Cylindrical map shape

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Cylindrical map shape

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Spherical map shape

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Spherical map shape

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Spherical map shape

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Cube map shape

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Cube map shape

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What do we get from the texture?

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Parametric patches

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Parametric patches

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Parametric patches

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Parameterized cube

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Non-linear mapping

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Triangular meshes

  • One texture coordinate per vertex
  • Regular parameterization of the mesh
  • Requirements:

– Continuous – Small angular deformations – Small area deformations – Covers the entire mesh – In practice: at most two

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Triangular mesh example

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Singularities (poles)

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Bump mapping

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Examples

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Bump mapping

  • Input = normal map (nx, ny, nz)
  • Local frame:

– z = geometric normal – x,y = tangent, bitangent

Follow the texture coordinates!

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Bump mapping

  • Example : note how blue (z) is dominant
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Bump mapping

  • Shading normal : local frame
  • Light, eye: global frame
  • Move everything to the same frame
  • [TBN]: transformation matrix

– To inverse, or not to inverse?

  • Note:

– textures in [0,1]3 – normals in [-1,1]3

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Bump mapping

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Displacement mapping

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Displacement mapping: how?

  • Not in the fragment shader

– Except towards the inside? – Candidate for tesselation shader

  • Easier with other rendering methods

– ray-tracing

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Relief textures

  • displacement mapping extreme case
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Relief textures

  • How?
  • Warp textures before mapping
  • Or follow rays in a height field
  • Polygons = convex hull
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Environment mapping

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Raytracing/Env. mapping

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Raytracing/Env. mapping

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Environment mapping

  • Texture = distant light
  • Parameterization: cube, sphere
  • Incoming ray + reflection = outgoing ray
  • Query texture in this direction
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Environment mapping

Example environment map (spherical parameterization)

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Environment mapping

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Environment mapping

  • Can also work with refracted rays
  • Only one interface

– huge approximation

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Environment mapping

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Environment mapping

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Aliasing

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Under-sampling

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Need pre-filtering

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Multiple samples per pixel

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Aliasing

  • Texture + distance = aliasing

– Looks bad – Multi-sampling is not enough

  • Color textures: can pre-filter
  • Normal maps, height maps:

– Pre-filtering doesn’t make sense – Open research problem

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3d textures

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3D parameterization

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Examples: distance to a plane

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Distance to a line

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Color ramps, sinus…

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Color-table

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Noise is useful

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Simplex noise

  • Same as gradient noise
  • Use a simplex instead of a cube
  • 3D: tetrahedron + gradient interpolation
  • Underlying structure is invisible

http://en.wikipedia.org/wiki/Simplex_noise

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Frequency

8 16 32

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5 octaves together

Persistence = 0.5

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5 octaves together

Persistence = 0.2

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Noise

  • Parameters :

– Number of octaves – Amplitude of first octave – Persistence: ratio amplitude octaves

  • Geometric sequence

– Lacunarity: ratio of octave periods

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Noise

  • Often compared to salt in cooking
  • Only noise: not very good
  • 3D textures without noise: a bit bland
  • Combination textures 3D + noise

– Really interesting

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Procedural textures

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Perturbations

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Procedural textures + noise

  • Not limited to color
  • Normals, material parameters...
  • Regular structure + a bit of noise

– Wood, bricks, floor tiles...

  • Filtering / anti-aliasing : harder, but

necessary

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Procedural textures for object definition

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All together...