Maths

1
Maths Technologies for GamesDirectX 11 New
FeaturesTessellation Displacement Mapping

• CO3303
• Week 19

2
Todays Lecture

1. Direct3D 11 New features
2. Direct3D 11 Changes from Direct3D 10
3. New DX11 Pipeline
4. Tessellation Overview
5. Patches
6. Details Hull Shader / Tessellation Stage /
   Domain Shader
7. Displacement Mapping
8. Technical Considerations and Issues

3
DirectX 11 New Features

• DirectX 11 was introduced with Windows 7
• But is also supported on Windows Vista
• Major new features introduced in DX11
• Multithreaded rendering
• A single device can have several contexts
• Different threads that can render using the same
  resources
• Tessellation
• Introduced in this lecture
• Compute Shaders
• General purpose (non-graphics) programming on the
  GPU
• More recently, support has been added for DX10
  hardware
• Shader Model 5.0 extra shader language features
• High quality texture compression formats

4
Converting from DX10 to DX11

• DirectX 11 is a strict superset of DX10.1
• Nearly everything in DX10 works with minimal
  change
• Not like the huge changes from DX9 to DX10
• Key points when converting
• The device pointer (g_pD3DDevice) has been split
  in two
• A device pointer for overall control a context
  pointer for each thread
• Use the immediate context pointer for single
  threaded work
• Context pointer used for most rendering Draw,
  SetXXShader etc.
• The Effects framework (.fx) is not in the
  provided libraries
• Compile it ourselves (add an extra Effects11
  project to our solution)
• DX maths libraries not in 11, now provided as an
  extra download
• No font support in the D3DX libraries (now an
  extra download)
• Or use Direct2D, DirectWrite, or a 3rd party
  library
• Minor changes to a few DX structures require code
  tweaks

5
New DX11 Pipeline Stages

• In order to support tessellation, DX11 adds three
  new stages to the rendering pipeline
• Two programmable stages
• Hull Shader
• Domain Shader
• One fixed stage in between
• Tessellation stage
• No shader
• All three must be used together
• Only used when tessellating
• Disabled otherwise

6
Tessellation - Overview

• Input geometry is made of patches and control
  points
• Not strictly vertices and polygons
• Each patch has several control points, from 1 to
  32
• The vertex shader processes each control point
• Likely to convert into world space
• But probably not into viewport space since they
  are not ready for rendering
• The hull shader also processes each control point
• But can access all points for a patch
• Used for patch-specific transforms

7
Tessellation - Overview

• Hull shader has an associated patch constant
  function
• Called once per patch
• Determines the amount of tessellation required
  for that patch
• The tessellation stage tessellates the patch as
  required
• Tessellation occurs in generic 0-gt1 space, not
  world space
• The domain shader takes the generic tessellation
  and control points and creates final vertices
• Which are sent to the geometry / pixel shaders as
  normal

Tessellation Stage Generic tessellations with
different tessellation factors
Domain Shader Control points shape the generic
tessellation to create final mesh
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Patches / Control Points

• Model geometry for tessellation uses patches and
  control points
• A patch is a line, triangle or quad, which is
  bent or shaped by some number of control points
• For example, a Bezier spline
• DirectX does not specify the available patch
  types
• We can choose any and implement it in hull and
  domain shaders
• This is potentially a huge change for game asset
  creation
• Patches suit artwork creation much better than
  polygonal modelling

A quad patch and control points
Head made from quad patches
9
Hull Shader

• The hull shader gets access to all the control
  points for a single patch and can process them in
  any way
• It outputs the final control points used to shape
  the patch
• It can output greater or fewer control points if
  necessary
• For many tessellation purposes, we dont need to
  change the control points given
• Often the vertex shader converts to world space
  theyre ready
• So many hull shaders just copy input to output
• However, they can be used for advanced purposes
• Approximating complex input splines using simpler
  output splines
• Providing per-control-point information to help
  the patch constant function (see next slide)

10
Patch Constant Function

• The patch constant function is called once per
  patch
• It must decide how much to tessellate each patch
• It can also output other custom per-patch data
• It can access the input control points and the
  hull shader ouput control points (as arrays) to
  do its job
• Patch tessellation is specified as one Interior
  Tessellation Factor and three or four Edge
  Tessellation Factors
• That is for a triangle or quad patch. A line only
  has one factor
• These factors specify how much to divide the
  edges and split up the interior of each patch
  (see next slides)
• A simple patch constant function can just set
  fixed values
• More commonly the factors are increased as models
  get nearer, or for more complex areas of the
  geometry

11
Tessellation Stage

• The tessellation stage uses the factors specified
  in the patch constant function
• Divides up a unit square, triangle or line based
  on the factors
• It works in a generic 0-gt1 space
• Usually referred to with UV axes
• Outputs this generic geometry as vertices for the
  domain shader next
• Several fixed algorithms are available for the
  tessellation
• Specify in the hull shader code

Edge Factors 3,1,1,1Interior Factors
1,1(Horizontal / Vertical)
Edge Factors 1,1,1,1Interior Factors 4,4
Edge Factors 4,4,4,4Interior Factors 4,4
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Domain Shader

• The domain shader
• Takes control points output from the hull shader
• And the generic vertices output from the
  tessellation stage
• Combine to create final tessellation for the
  scene
• Exactly what this involves depends on the patch
  type
• At least involves transforming generic vertices
  to world space
• Then some manipulation based on the control points

Five Control points shaping a tessellated
quad Number of control points and formula used
for shaping decided by programmer, e.g. NURBs
Catmull-Clark surfaces, etc.
13
Distance / Density Variation

• It is common to vary the amount of tessellation
  used based on the geometry distance or complexity
  (density)
• Distance variation is simpler
• The patch control function can look at the
  distance of the control points to the camera
• Make tessellation factor decisions based on that
• Density variation needs pre-processing
• The patch control function can get an integer ID
  for each patch
• So analyse the complexity of each patch offline
• Store complexity in an array (1D texture) indexed
  by patch ID
• Patch control function reads this array to choose
  tessellation factors

14
Water-tight Patch Seams

• As soon as we vary tessellation per-patch, there
  are problems with patch seams
• Cracks in the geometry appearing at the edges
  between patches of different tessellation
• That is why we can control the edge tessellation
  separately
• Ensure all edges have the same tessellation
  factor in the patch on each side (watertight
  seams)
• Additional processing for the patch constant
  function / hull shader

Adjacent patches, different tessellation causes
crack at seam
Match edge tessellation to create watertight
seams
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Displacement Mapping

• Displacement mapping is adjusting the height of
  vertices based on heights stored in a texture (a
  height map)
• Effectively, this is parallax mapping done
  properly
• Result has correct silhouettes and no visual
  problems
• Requires finely detailed geometry, so it works
  well with tessellation
• A very effective method to provide fine geometry
  detail with less expense and to make most
  effective use of the tessellation
• Can be used on most kinds of patch

Parallax Mapping
Tessellation Height Map
Displacement Mapping
16
Displacement Mapping

• Control points and patches seem far from a games
  polygonal models
• But, can use displacement mapping and
  tessellation on polygons too
• Call each triangle a patch
• Call the three vertices control points
• Use tessellation to create interior vertices and
  triangles
• Hull shader just copies control points
• Domain shader transforms generic tessellated
  triangle to position of original triangle
  tangent-space work for this
• Displacement mapping on result vertices
• Need height map for displacement and a normal map
  for lighting
• Same requirements as parallax mapping

Triangle TessellationUsed on polygonal mesh
17
Technical Issues

• Tessellation has performance implications
• A very efficient method to draw large number of
  polygons
• However, minimise it dont tessellate
  off-screen, use lower tessellation in the
  distance, fall back to normal mapping etc.
• Displacement mapping brings more seam issues
• Any discontinuity in texture, e.g. where two
  different textures meet, will cause a
  discontinuity in displacement (i.e. cracks)
• Even with the most careful mapping, this cannot
  be avoided
• Solve by specifying a dominant texture at patch
  seams
• Extra coding in the hull shader / patch constant
  function
• Sharp edges cause cracks (use normal map or
  averaging at edges)
• Models must be designed with displacement in mind
• Very low polygon models wont work well. Start
  with the basic shape of the height map designed
  into the geometry (see lab)

18
Future for Tessellation in Games

• Will see tessellation / displacement mapping on
  standard polygonal models in the lab
• However, these technologies allow us to start
  using patch / control point based geometry
  instead
• Artists have long used patch-basedmodelling for
  commercial animation
• Catmull-Clark subdivision surfacesare quite well
  suited to GPU tessellation
• A low polygon surface that mathematically defines
  a curved patch
• There have been a few experiments with these in
  games already, expect to see variants of these
  used more frequently
• The polygon is dead (soon)