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computer graphics • texture mapping © 2006 fabio pellacini • 1
texture mapping
computer graphics • texture mapping © 2006 fabio pellacini • 2
why texture mapping?
• objects have spatially varying details• represent as geometry: correct, but very expensive
computer graphics • texture mapping © 2006 fabio pellacini • 3
why texture mapping?
• use simple geometry• store varying properties in images• map to objects
[Wol
fe /
SG97
Slid
e se
t]
computer graphics • texture mapping © 2006 fabio pellacini • 4
why texture mapping?
• produces compelling results
[Jere
my
Birn
]
computer graphics • texture mapping © 2006 fabio pellacini • 5
why texture mapping?
• easily change object appearance
[Pra
unet
al.,
200
1]
computer graphics • texture mapping © 2006 fabio pellacini • 6
mapping function
• surfaces are 2d domains• determine a function that maps them to images
MappingFunction
Surface Image
computer graphics • texture mapping © 2006 fabio pellacini • 7
mapping functions – projections
• maps 3d surface points to 2d image coordinates
• different types of projections– often corresponding to simple shapes– useful for simple object
23 ]1,0[: →ℜf
[Wol
fe /
SG97
Slid
e se
t]
computer graphics • texture mapping © 2006 fabio pellacini • 8
projections – planar
computer graphics • texture mapping © 2006 fabio pellacini • 9
projections – cubical
computer graphics • texture mapping © 2006 fabio pellacini • 10
projections – cylindrical
computer graphics • texture mapping © 2006 fabio pellacini • 11
projections – spherical
computer graphics • texture mapping © 2006 fabio pellacini • 12
projections
• planar projection along xy plane of size (w,h)– use affine transform to orient the plane differently
• spherical projection of unit sphere– consider point in spherical coordinates
• cylindrical projection of unit cylinder of height h– consider point in cylindrical coordinates– treat caps separately
)/,/()( hpwpf yx=p
),()( θφ=pf
)/,()( hpf yφ=p
computer graphics • texture mapping © 2006 fabio pellacini • 13
looking up texture values
• normal: do not repeat texture– clamp image coordinates to [0,1] then lookup
• tiled: repeat texture multiple times– take mod of image coordinates then lookup
normal tiled
computer graphics • texture mapping © 2006 fabio pellacini • 14
texture mapping artifacts
• tiling textures might introduce seems– discontinuities in the mapping function– change texture to be “tileable” when possible
computer graphics • texture mapping © 2006 fabio pellacini • 15
texture mapping artifacts
• mapping textures will introduce distortions– unavoidable artifacts
• local scale and rotation differences
distorted undistorted
computer graphics • texture mapping © 2006 fabio pellacini • 16
mapping function – explicit coordinates
• store texture coordinates on control points• interpolate as any other parameter
– follow interpolation rule defined by surface type
• parametric surfaces: can use parameters directly
• known as UV mapping
computer graphics • texture mapping © 2006 fabio pellacini • 17
uv mapping subdivision surfaces
level 0 level 1 level 2
computer graphics • texture mapping © 2006 fabio pellacini • 18
uv mapping vs. projection
parameterization projection
computer graphics • texture mapping © 2006 fabio pellacini • 19
uv mapping parametric surfaces
[Wol
fe /
SG97
Slid
e se
t]
computer graphics • texture mapping © 2006 fabio pellacini • 20
uv mapping polygon meshes
computer graphics • texture mapping © 2006 fabio pellacini • 21
uv mapping polygon meshes
[Pip
onie
t al
., 20
00]
computer graphics • texture mapping © 2006 fabio pellacini • 22
uv mapping polygon meshes
• break up model intro single texture
[©D
iscr
eet]
computer graphics • texture mapping © 2006 fabio pellacini • 23
interpolating uv coordinates on meshes
• pay attention when rasterizing triangles– for raytracing just use baricentric coordinates
texture linear interp. perspective interp.
used also for colors
[MIT
Ope
nCou
rsew
are]
computer graphics • texture mapping © 2006 fabio pellacini • 24
painting textures on models
• if painting is required, paint directly on surfaces– system determines inverse mapping to update image– seems/distortions present, but user does not know
computer graphics • texture mapping © 2006 fabio pellacini • 25
texture magnification
• linearly interpolate closest pixels in texture
[MIT
Ope
nCou
rsew
are]
texture rendered image
computer graphics • texture mapping © 2006 fabio pellacini • 26
texture minification
• compute average of texture pixels projected onto each view pixels
[MIT
Ope
nCou
rsew
are]
texture rendered image
computer graphics • texture mapping © 2006 fabio pellacini • 27
texture minification
• remember point-sampling introduces artifacts– need average of texture below a pixel
[MIT
Ope
nCou
rsew
are]
computer graphics • texture mapping © 2006 fabio pellacini • 28
mip-mapping
• approximate algorithm for computing filters• store texture at different resolution• look up the appropriate image based on its projected
size
[MIT
Ope
nCou
rsew
are]
computer graphics • texture mapping © 2006 fabio pellacini • 29
3d solid texturing
• define a 3D field of values, indexed using P– in-memory array: too much memory– procedurally: hard to define
• often add noisy-like details on 2d images
[Wol
fe /
SG97
Slid
e se
t]
computer graphics • texture mapping © 2006 fabio pellacini • 30
types of mapping
computer graphics • texture mapping © 2006 fabio pellacini • 31
texture mapping material parameters
• diffuse coefficient
computer graphics • texture mapping © 2006 fabio pellacini • 32
texture mapping material parameters
• specular coefficient
computer graphics • texture mapping © 2006 fabio pellacini • 33
displacement mapping
• variations of surface positions, thus normals– requires fine tessellation of object geometry
computer graphics • texture mapping © 2006 fabio pellacini • 34
displacement mapping
• update position by displacing points along normal
• recompute normals by evaluating derivatives– no closed form solution: do it numerically
NPP hd +=
vuvudddd
d ΔΔ
×ΔΔ
≈∂∂
×∂∂
∝PPPPN
computer graphics • texture mapping © 2006 fabio pellacini • 35
bump mapping
• variation of surface normals– apply normal perturbation without updating positions
computer graphics • texture mapping © 2006 fabio pellacini • 36
bump mapping
• simple example: bump mapping xy plane
zyxNPP),(),(),(),(
vuhvuvuhvuvud
++==+=
yxz
zyzxPPN
vh
uh
vh
uh
vudd
d
∂∂
−∂∂
−=
=⎟⎠⎞
⎜⎝⎛
∂∂
+×⎟⎠⎞
⎜⎝⎛
∂∂
+=∂∂
×∂∂
∝
computer graphics • texture mapping © 2006 fabio pellacini • 37
bump vs. displacement mapping
bump map displacement map
computer graphics • texture mapping © 2006 fabio pellacini • 38
bump vs. displacement mapping
bump map displacement map
computer graphics • texture mapping © 2006 fabio pellacini • 39
combining maps types
• combine multiple maps to achieve realistic effects
computer graphics • texture mapping © 2006 fabio pellacini • 40
lighting effects using texture mapping
computer graphics • texture mapping © 2006 fabio pellacini • 41
shadow mapping
• graphics pipeline does not allow shadow queries• we can use texturing and a multipass algorithm
project a color texture “project” a depth texture
[NV
IDIA
/Eve
ritt
et a
l.]
computer graphics • texture mapping © 2006 fabio pellacini • 42
shadow mapping algorithm
• pass 1: render scene from light view• pass 1: copy depth buffer in a new texture
• pass 2: render scene from camera view• pass 2: transform each pixel to light space• pass 2: compare value to depth buffer• pass 2: if current < buffer depth then shadow
computer graphics • texture mapping © 2006 fabio pellacini • 43
shadow mapping algorithm
[NV
IDIA
/Eve
ritt
et a
l.]
camera view light view shadow buffer
computer graphics • texture mapping © 2006 fabio pellacini • 44
shadow mapping algorithm
[NV
IDIA
/Eve
ritt
et a
l.]
camera view light distance projected shadow buffer
computer graphics • texture mapping © 2006 fabio pellacini • 45
shadow mapping limitations
• not enough resolution: blocky shadows– pixels in shadow buffer too large when projected
• biasing: surfaces shadow themselves– remember the epsilon in raytracing– made much worst by resolution limitation
[Fernando et al., 2002]
computer graphics • texture mapping © 2006 fabio pellacini • 46
environment mapping
• graphics pipeline does not allow reflections• we can use texturing and a multipass algorithm
[Wol
fe /
SG97
Slid
e se
t]
computer graphics • texture mapping © 2006 fabio pellacini • 47
environment mapping algorithm
• pass 1: render scene 6 times from object center• pass 1: store images onto a cube
• pass 2: render scene from the camera view• pass 2: use cube projection to look up values
• variation of this works also for refraction
computer graphics • texture mapping © 2006 fabio pellacini • 48
environment map limitations
• incorrect reflections– objects in incorrect positions: better for distant objs– “rays” go through objects
• inefficient: need one map for each object
computer graphics • texture mapping © 2006 fabio pellacini • 49
light effects take home message
• pipeline not suitable for lighting computations– algorithms are complex to implement and not robust
• lots of tricks and special cases
– but fast
• interactive graphics: use pipeline algorithms• high-quality graphics: use pipeline for view, raytracing
for lighting
computer graphics • texture mapping © 2006 fabio pellacini • 50
texturing demosOpenGL tutor:
texture.exe
NVidia samples:bumpy_shiny_patch.exe
hw_shadowmap_simple.exesimple_soft_shadows.exe