texture mapping - fabio...
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![Page 1: texture mapping - Fabio Pellacinipellacini.di.uniroma1.it/teaching/graphics09/lectures/13_Texturing.pdf · • tiling textures might introduce seems – discontinuities in the mapping](https://reader034.vdocuments.us/reader034/viewer/2022042918/5f5f98a5f869ea1e9050826d/html5/thumbnails/1.jpg)
computer graphics • texture mapping © 2009 fabio pellacini • 1
texture mapping
computer graphics • texture mapping © 2009 fabio pellacini • 2
why texture mapping?
• objects have spatially varying details • represent as geometry: correct, but very expensive
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computer graphics • texture mapping © 2009 fabio pellacini • 3
why texture mapping?
• use simple geometry • store varying properties in images • map to objects
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computer graphics • texture mapping © 2009 fabio pellacini • 4
why texture mapping?
• produces compelling results [Je
rem
y Bi
rn]
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computer graphics • texture mapping © 2009 fabio pellacini • 5
why texture mapping?
• easily change object appearance
[Pra
un e
t al
., 20
01]
computer graphics • texture mapping © 2009 fabio pellacini • 6
mapping function
• surfaces are 2d domains • determine a function that maps them to images
Mapping Function
Surface Image
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computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 8
projections – planar
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computer graphics • texture mapping © 2009 fabio pellacini • 9
projections – cubical
computer graphics • texture mapping © 2009 fabio pellacini • 10
projections – cylindrical
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computer graphics • texture mapping © 2009 fabio pellacini • 11
projections – spherical
computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 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 © 2009 fabio pellacini • 14
texture mapping artifacts
• tiling textures might introduce seems – discontinuities in the mapping function – change texture to be “tileable” when possible
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computer graphics • texture mapping © 2009 fabio pellacini • 15
texture mapping artifacts
• mapping textures will introduce distortions – unavoidable artifacts
• local scale and rotation differences
distorted undistorted
computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 17
uv mapping subdivision surfaces
level 0 level 1 level 2
computer graphics • texture mapping © 2009 fabio pellacini • 18
uv mapping vs. projection
parameterization projection
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computer graphics • texture mapping © 2009 fabio pellacini • 19
uv mapping parametric surfaces
[Wol
fe /
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computer graphics • texture mapping © 2009 fabio pellacini • 20
uv mapping polygon meshes
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computer graphics • texture mapping © 2009 fabio pellacini • 21
uv mapping polygon meshes
[Pip
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., 20
00]
computer graphics • texture mapping © 2009 fabio pellacini • 22
uv mapping polygon meshes
• break up model intro single texture [©
Dis
cree
t]
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computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 25
texture magnification
• linearly interpolate closest pixels in texture
[MIT
Ope
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are]
texture rendered image
computer graphics • texture mapping © 2009 fabio pellacini • 26
texture minification
• compute average of texture pixels projected onto each view pixels
[MIT
Ope
nCou
rsew
are]
texture rendered image
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computer graphics • texture mapping © 2009 fabio pellacini • 27
texture minification
• remember point-sampling introduces artifacts – need average of texture below a pixel
[MIT
Ope
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computer graphics • texture mapping © 2009 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
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are]
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computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 30
types of mapping
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computer graphics • texture mapping © 2009 fabio pellacini • 31
texture mapping material parameters
• diffuse coefficient
computer graphics • texture mapping © 2009 fabio pellacini • 32
texture mapping material parameters
• specular coefficient
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computer graphics • texture mapping © 2009 fabio pellacini • 33
displacement mapping
• variations of surface positions, thus normals – requires fine tessellation of object geometry
computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 35
bump mapping
• variation of surface normals – apply normal perturbation without updating positions
computer graphics • texture mapping © 2009 fabio pellacini • 36
bump mapping
• simple example: bump mapping xy plane
zyxNPP),(),(),(),(vuhvuvuhvuvud
++=
=+=
yxz
zyzxPPN
vh
uh
vh
uh
vudd
d
∂∂
−∂∂
−=
=⎟⎠⎞
⎜⎝⎛
∂∂
+×⎟⎠⎞
⎜⎝⎛
∂∂
+=∂∂
×∂∂
∝
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computer graphics • texture mapping © 2009 fabio pellacini • 37
bump vs. displacement mapping
bump map displacement map
computer graphics • texture mapping © 2009 fabio pellacini • 38
bump vs. displacement mapping
bump map displacement map
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computer graphics • texture mapping © 2009 fabio pellacini • 39
combining maps types
• combine multiple maps to achieve realistic effects
computer graphics • texture mapping © 2009 fabio pellacini • 40
lighting effects using texture mapping
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computer graphics • texture mapping © 2009 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
al.]
computer graphics • texture mapping © 2009 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
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computer graphics • texture mapping © 2009 fabio pellacini • 43
shadow mapping algorithm
[NV
IDIA
/Eve
ritt
et
al.]
camera view light view shadow buffer
computer graphics • texture mapping © 2009 fabio pellacini • 44
shadow mapping algorithm [N
VID
IA/E
veri
tt e
t al
.]
camera view light distance projected shadow buffer
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computer graphics • texture mapping © 2009 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 © 2009 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]
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computer graphics • texture mapping © 2009 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 © 2009 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
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computer graphics • texture mapping © 2009 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 © 2009 fabio pellacini • 50
texturing demos OpenGL tutor:
texture.exe
NVidia samples: bumpy_shiny_patch.exe
hw_shadowmap_simple.exe simple_soft_shadows.exe