CM0304 Graphics I Graphics Hardware I.1 Graphics Systems
CMT107 Visual Computing
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IV.2 Polygon Shading
Xianfang Sun
School of Computer Science & Informatics
Cardiff University
➢ Shading polygons
• Flat shading
• Gouraud shading
• Phong shading
➢Special effects
• Transparency
• Refraction
• Atmospheric effects
➢OpenGL Shading
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➢ The colour of 3D objects is not the same everywhere
• An object drawn in a single colour appears flat
• Light-material interactions cause each point to have a
different colour or shade in 3D
➢ Global shading requires to calculate all reflections between
all objects
• In general this is not computable
➢ We use a simplified local model: Phong illumination
Polygon Shading
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➢ Use Phong Illumination for polygon shading
(e.g. with scan-line to set colours of pixels)
• Need to compute surface normals
• Polygon approximates 3D shape
(normals may not be normals of actual polygon)
➢ Different approaches to polygon shading:
− Flat shading
− Gouraud shading
− Phong shading
Flat Shading
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➢ One illumination calculation per polygon
• Each pixel is assigned the same colour
• Usually computed for centroid of polygon:
➢ Good for polyhedral objects, but:
• For point light sources, direction to light varies
• For specular reflections, direction to eye varies
Vertex Normals
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➢ Introduce surface normals for each vertex
• Usually different from polygon normal
• Either exact normals of surface
• Or average of normals of polygons meeting at a vertex
(good if polygons approximate surface well)
Gouraud Shading
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➢ Compute illumination for vertices of polygon
• Use vertex normals
• Linearly interpolate colours between vertices
Gouraud Shading Interpolation
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➢ Bilinearly interpolate colours between vertices down and
across scan lines
A = (1-)I1+I3
B = (1-)I2+I3
I = (1-)A+B
Gouraud Shading Example
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➢ Creates smoothly shaded polygonal mesh
➢ Artefacts still visible
➢ Need a fine mesh to capture subtle lighting effects
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➢ One lighting calculation per pixel
• Linearly interpolate vertex normals across polygon
➢ Very smooth appearance, but artefacts along silhouettes
➢ Do not confuse with Phong illumination model!
Interpolation
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➢ Bilinear interpolation of normals from vertices
Interpolation
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➢ Bilinear interpolation of normals from vertices
A = (1-)N1+N3
B = (1-)N2+N3
N = (1-)A+B
Shading Notes
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➢ Be careful when transforming surface normals
• Normals are not points, but a surface property
• Point transformations are different from normal
transformations
(point transformation A becomes (A-1)t for normals)
➢ Advanced shaders implemented on GPU in OpenGL SL
Transparency
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➢ Opacity coefficient k tells how much light is blocked:
➢ I = kIreflected + (1 – k)Itransmitted
• k [0,1]: 0 for transparent surface, 1 for opaque surface
• Ireflected is intensity of reflected light
• Itransmitted is intensity of transmitted light from behind the
➢ Requires expansion of visible surface detection to access
polygons further behind
• Use A buffer
Snell’s Law
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➢ Refraction direction required for physically correct
transparency computation
➢ Snell’s law
−= coscos
= sinsin
Snell’s Law
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Vector decomposition:
where S is a vector on the horizontal direction.
−−= sincos NT
−= coscos
= sinsin
+= sincos NL ( )NL
➢ Refraction of light through glass
• Emerging refracted ray travels along a path parallel to
incoming light ray
➢ Usually ignore refraction
• Assume light travels straight through surface
(good approximation for thin polygonal surfaces)
Refraction
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No Refraction With Refraction
Refraction Example
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➢ Similar to transparency, modify light intensities for fog,
smoke, etc.
I = fatmo(d)Iobject + (1 – fatmo(d))Iatmo
• Iobject is intensity from visible object
• Iatmo is intensity for atmospheric effect
• fatmo(d) is function modelling atmospheric effect
depending on distance d from viewer, e.g.:
fatmo,1(d) = e
fatmo,2(d) = e
fatmo,3(d)= (End-d)/(End-Start)
Atmospheric Effects
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OpenGL Shading
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➢ Fixed-function pipeline version of OpenGL uses specific
functions to realise flat and Gouraud shading,
transparency, and fog effect
➢ Shader version of OpenGL needs the programmer to
write code in the main program and/or the shaders to
implement these effects
➢More details in the labs …
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➢ How does flat, Gouraud, Phong shading for polygons
work? What are the differences / similarities between the
different shading algorithms?
➢ Why do we need explicit surface normals for vertices?
➢ How can we add transparency and atmospheric effects to
our lighting computations?
➢ What is refraction / Snell’s law?
➢ Why is refraction usually ignored?
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