PV227 GPU programming
Marek Vinkler
Department of Computer Graphics and Design
Points and vectors
• points (before projection) are quadruples: (x, y, z, 1.0),
• can be transformed with a 4 x 4 matrix,
• vectors are also quadruples: (x, y, z, 0.0),
• can be transformed with a4x4or3x3 matrix.
4 □ ►  4 fi> ► 4
PV227 GPU programming
Normal transformation
a points are transformed to eye space with modelview matrix,
• vectors constructed from points (e.g. P2 - Pi) are also transformed with this matrix,
• normals are not!
Normal transformation
Normal transformation
• caused by non-uniform scale,
• we need another matrix (N) for transforming normal n,
• M is the modelview matrix, Ms tangent vector P2 - and / is identity.
(M x t) ■ {N x n) = 0 (Mxt)T x (Nx n) = 0 TrxMTxNxn = 0
PV227 GPU programming
5/23
Normal transformation
tTxMTxNxn = 0 t-n = 0^tTxn = O^MTxN=l
MT x N= I (M7)-1 x MT x N = (Mr)~1 N= (M7)-1
PV227 GPU programming
6/23
Normal transformation
a N is inverse transpose of M (3 x 3 submatrix of M),
• for orthogonal matrices AT = A~1, rotation is orthogonal,
• M is orthogonal M = (M7) 1    A/ = M.
Renormalization
• normals must be of unit length,
• can be destroyed by normal transformation ->• must be normalized in vertex shader,
• interpolation can also destroy vector length ->- must be normalized in fragment shader.
Figure: Taken from lighthouse3d.com
Lighting
• computation of light's interaction with surfaces,
• huge cheat,
a ambient, diffuse and specular light,
• flat, gouraud and phong lighting,
• directional, point and spot light,
• no shadow, no bouncing of light.
Ambient lighting
• approximates lighting after infinite number of bounces,
• homogeneous,
• prevents black areas that look unnatural,
• usually chosen as fraction of the diffuse (material) color,
• l = Ka.
PV227 GPU programming
Figure: Ambient spheres □ ► *o ► < s ► < i ►  i -o<ko
10/23
Directional light
Figure: Taken from lighthouse3d.com
• far away light,
• defined by a direction vector (position is irelevant),
• can represent e.g. the sun.
Gouraud shading
• per vertex lighting,
• interpolation of vertex colors,
• unable to capture lighting details inside polygons.
Diffuse lighting
• simulate light's interaction with perfectly diffuse material,
• angle dependent,
• significant color component,
• / = cos(a) x Kd.
Figure: Diffuse spheres
Diffuse lighting
Figure: Taken from lighthouse3d.com
• amount of incoming light diminishes with increasing angle,
• normalized vectors: / = (I • N) x Kd,
• all vectors must be in same space, usually defined in world space, computation in camera space.
PV227 GPU programming
14/23
Flat shading
• per vertex lighting,
• no interpolation,
• unable to capture smooth changes in light intensity.
Figure: Flat shading
Combined lighting
• light from various sources can be combined (added),
• combination of ambient and diffuse prevents black areas,
• I = Ka + cos(a) x Kd,
• value should not be outside the [0.0,1.0] range.
Figure: Ambient + Diffuse spheres
Specular lighting
• simulate light's interaction with reflective material,
• angle dependent,
• highlight of the light's color, not material color,
• / = cos(/3)s x Ks, s controls size of the highlight.
Figure: Specular spheres (Phong vs Blinn-Phong)
Phong lighting
L      *W R
L \ a
N
a
d = L|cos(a) !
Eye
3>
-L
Figure: Taken from lighthouse3d.com
• amount of reflected light diminishes with increasing angle,
• R = -L + 2(N-L) x N,
• cos(/3) = R ■ Eye,
• all vectors must be in same space, normalized.
PV227 GPU programming
18/23
Blinn-Phong lighting
Figure: Taken from lighthouse3d.com
• amount of reflected light diminishes with increasing angle,
• H = L + Eye,
• cos(/3) = H ■ N,
• all vectors must be in same space, normalized.
PV227 GPU programming
Combined lighting
• light from various sources can be combined (added),
• ambient, diffuse and specular form the baseline lighting,
• l = Ka + cos(a) x Kd + cos(/3)s x Ks,
• value should not be outside the [0.0,1.0] range.
Figure: Ambient + Diffuse + Specular pawns
Phong shading
• per pixel lighting,
• smooth lighting including details,
• interpolation of vertex attributes (normal, eye, light).
Figure: Per pixel lighting pawns
Point light
• light source inside the scene,
• defined by a position vector (all directions),
• can represent e.g. a lightbulb.
Figure: Point light pawns, Taken from lighthouse3d.com
PV227 GPU programming
22/23
Spot light
• light source inside the scene,
• only a directed cone is illuminated,
• defined by a position vector, direction vector and angle,
• can represent e.g. a flashlight.
Figure: Spot light pawns
PV227 GPU programming
23/23