6.1Vis_04

Data VisualizationData Visualization

Lecture 6-

A Rough Guide to Rendering

6.2Vis_04

Rendering of TrianglesRendering of Triangles

Surface views for 2D scalar visualization, and isosurfaces for 3D scalar visualization both generate a triangular mesh surface

Techniques for rendering these meshes rely on :– an understanding of how light is

reflected from surfaces - to define the colour of points within each triangle

– generating a 2D image representation of the 3D scene

Just a simplified view here...

6.3Vis_04

Reflection ModelReflection Model

There are two major components to consider in modelling reflection of light from a surface– diffuse reflection: this gives a dull

effect; light is scattered evenly and gives the colour of the surface

– specular reflection: this gives shininess of surface; light is reflected at angle of perfect reflection and has colour of incoming light

– total effect is sum of both (plus ambient light)

6.4Vis_04

* intensity of reflected lightdepends on angle of light to surface

Reflection Model - Diffuse Reflection

Reflection Model - Diffuse Reflection

lightsourceN

L

I* = Intensity of light sourceN = Surface normalL = Direction of light sourceKd = Diffuse-reflectioncoefficient (gives colour)I = Reflected intensity

surface

I = Kd (cos ) I*

* equal reflection in all directions

I, I*, Kd have R, G, B components

6.5Vis_04

I* = Intensity of light sourceV = View directionR = Direction of perfect

reflected lightKs = Specular-reflection

coefficientI = Reflected intensity

I = Ks( cos )n I*

n varies with materiallarge n : shinysmall n : dull

Intensity depends on angle between eye and reflected light ray - and type of material

V

lightsourceN

LR

eye

surface

Reflection Model - Specular ReflectionReflection Model -

Specular Reflection

6.6Vis_04

Effect of Diffuse ReflectionSlide from Alan Watt, University of Sheffield

Effect of Diffuse ReflectionSlide from Alan Watt, University of Sheffield

6.7Vis_04

Effect of Diffuse plus Specular Reflection

Slide from Alan Watt, University of Sheffield

Effect of Diffuse plus Specular Reflection

Slide from Alan Watt, University of Sheffield

6.8Vis_04

RenderingRendering

To render a scene composed of a number of surfaces (here triangles):

We can project the surfaces on to a viewing plane, determining which are visible to the eye, and assigning the colour as given by the lighting model

6.9Vis_04

Perspective ProjectionPerspective Projection

view plane

eye point

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Parallel ProjectionParallel Projection

view plane

direction ofprojection

6.11Vis_04

Triangle RenderingTriangle Rendering

Thus, by projecting the triangle vertices, we get position of triangle in image - how can we get the colour of pixels within the triangle?

There are three techniques of increasing complexity - and increasing realism– Flat shading– Gouraud shading– Phong shading

6.12Vis_04

Flat Shading of Triangular Mesh

Flat Shading of Triangular Mesh

Each point in a triangle given the same intensity

N1N2

N3

N4

Fast and simple- but intensitydiscontinuities at edges

Calculate intensityfor each trianglefrom reflection modelequations

6.13Vis_04

Gouraud Shading of Triangular Mesh

Gouraud Shading of Triangular Mesh

Aim is to shade mesh as though it were curved surface

Step 1: Approximate normal at each vertex in some way -

one possibility is to average the normals of surrounding triangles

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Gouraud Shading of Triangular Mesh

Gouraud Shading of Triangular Mesh

Step 2: Calculate the intensityat each vertex using the lightingmodel

I1

I2

I3

I1

I2

I3

Step 3: Calculate the intensityat any interior point by linearinterpolation in triangle

6.15Vis_04

Phong Shading of Triangular Mesh

Phong Shading of Triangular Mesh

N1

N2

N3

Step 1: As for Gouraud, estimatenormals at vertices

N1

N2

N3

Step 2: Estimate normal at aninterior point by linear interpolation

Step 3: Calculate intensity byapplying lighting model

6.16Vis_04

Comparison of TechniquesComparison of Techniques

Flat shading:– fast and simple, 1 lighting calc’n done per

triangle, all pixels given same intensity– discontinuity in intensity across edges

Gouraud shading– relatively fast, 1 lighting calc’n per vertex,

intensity linearly interpolated from vertex intensities - giving smooth appearance – now industry standard

Phong shading– slower, lighting calc’n for each pixel - giving

very smooth appearance – not supported in OpenGL

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Constant or Flat Shading -Each Polygon has Constant

Shade

Constant or Flat Shading -Each Polygon has Constant

Shade

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Gouraud ShadingGouraud Shading

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Phong ShadingPhong Shading

6.20Vis_04

Flat, Gouraud and Phong Shading

Slides from Alan Watt, University of Sheffield

Flat, Gouraud and Phong Shading

Slides from Alan Watt, University of Sheffield

6.21Vis_04

Rendering by Ray TracingRendering by Ray Tracing

An alternative to polygon projection is the concept of ray tracing

Very high quality rendering with global inter-reflections

6.22Vis_04

Rendering of IsosurfacesRendering of Isosurfaces

Isosurface algorithms generate triangular meshes which can be rendered as just described

Key is the estimation of vertex normals for Gouraud and Phong shading

One possibility is to construct the entire surface, then assign vertex normals as average of normals of surrounding triangles

6.23Vis_04

Rendering of IsosurfacesRendering of Isosurfaces

An alternative - generally preferred - is based on fact that surface normal is equal to the gradient vector of f

At (xi,yj,zk), df/dx = 0.5*(f i+1,j,k - f i-1,j,k) df/dy = 0.5*(f i,j+1,k - f i,j-1,k) df/dz = 0.5*(f i,j,k+1 - f i,j,k-1)

This gives us normals at all grid points,and then trilinear interpolation will givenormals at the triangle vertices