Constant Tiled Textures

1
Constant Tiled Textures
Mach Kobayashi Square USA
2
Plane
surface tile() Oi 1 Ci Oi (s, t,
0)
3
Textured Plane
surface tile(string tex "") Oi float
texture(tex3, s, t) Ci Oi texture(tex,
s, t)
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Tiled Textured Plane
surface tile(string tex "") float ss
mod(s 5, 1) float tt mod(t 5, 1) Oi
float texture(tex3, ss, tt) Ci Oi
texture(tex, ss, tt)
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Tiled Textured Plane
surface tile(string tex "") float ss
mod(s 5, 1) float tt mod(t 5, 1) Oi
float texture(tex3, ss, tt) Ci Oi
texture(tex, ss, tt)
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Constant Tiled Textured Plane

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

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Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

5.0
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Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

5.0
9
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

5.0
10
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

5.0
1.25
11
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

2.5
5.0
1.25
12
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

2.5
5.0
.75
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Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

2.5
5.0
.25
14
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

.5
5.0
.75
15
Constant Tiled Textured Plane
2.5

• how is this done?
• for each point, look at every tile
• calculate distance in world space
• look up texture

.5
5.0
.25
16
World Space Distance
2.5

• (s, t)
• (startS, startT)
• ss (s-startS) width,tt (t-startT) length
• ss (.5-.4) 2.5 .25,tt (.5-.4) 5.0 .5

5.0
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World Space Distance
2.5

• (s, t)
• (startS, startT)
• ss (s-startS) width,tt (t-startT) length
• ss (.5-.4) 2.5 .25,tt (.5-.4) 5.0 .5

5.0
(.5, .5)
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World Space Distance
2.5

• (s, t)
• (startS, startT)
• ss (s-startS) width,tt (t-startT) length
• ss (.5-.4) 2.5 .25,tt (.5-.4) 5.0 .5

(.4, .4)
5.0
(.5, .5)
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World Space Distance
2.5

• (s, t)
• (startS, startT)
• ss (s-startS) width,tt (t-startT) length
• ss (.5-.4) 2.5 .25,tt (.5-.4) 5.0 .5

(.4, .4)
5.0
(.5, .5)
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World Space Distance
2.5

• (s, t)
• (startS, startT)
• ss (s-startS) width,tt (t-startT) length
• ss (.5-.4) 2.5 .25,tt (.5-.4) 5.0 .5

(.4, .4)
.5
5.0
.25
(.5, .5)
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Calculating Length

• consider coordinates of polygon
• ?P/?t (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( world?, Deriv(P, t)))

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Calculating Length
P (0, 2.5, 0)

• consider coordinates of polygon
• ?P/?t (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( world?, Deriv(P, t)))

P (0, -2.5, 0)
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Calculating Length
P (0, 2.5, 0)(s, t) (0, 0)

• consider coordinates of polygon
• dP/dt (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( world?, Deriv(P, t)))

P (0, -2.5, 0)(s, t) (0, 1)
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Calculating Length
P (0, 2.5, 0)(s, t) (0, 0)

• consider coordinates of polygon
• dP/dt (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( world?, Deriv(P, t)))

P (1.875, .25, 0)
P (1.875, 0, 0)
P (0, -2.5, 0)(s, t) (0, 1)
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Calculating Length
P (0, 2.5, 0)(s, t) (0, 0)

• consider coordinates of polygon
• dP/dt (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( world?, Deriv(P, t)))

P (1.875, .25, 0)(s, t) (.75, 45)
P (1.875, 0, 0)(s, t) (.75, .5)
P (0, -2.5, 0)(s, t) (0, 1)
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Calculating Length
P (0, 2.5, 0)(s, t) (0, 0)

• consider coordinates of polygon
• dP/dt (0, -5.0, 0)
• consider coordinates of micro polygon
• dP/dt (0, -5.0, 0)
• length(vtransform( "world", Deriv(P, t)))

P (1.875, .25, 0)(s, t) (.75, 45)
P (1.875, 0, 0)(s, t) (.75, .5)
P (0, -2.5, 0)(s, t) (0, 1)
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Constant Tiled Textured Plane
surface tile( string tex "" ) float
dPdsLength length(vtransform("world",
Deriv(P,s))) float dPdtLength
length(vtransform("world", Deriv(P,t))) Oi
0 float startS, startT for (startS 0
startS lt 1 startS .2) for (startT 0 startT
lt 1 startT .2) float ss (s - startS)
dPdsLength float tt (t - startT)
dPdtLength if (ssgt0 sslt1 ttgt0
ttlt1) float tileAlpha texture(tex3,
ss, tt) color tileColor texture(tex, ss,
tt) Ci (1 - Oi) tileAlpha
tileColor Oi (1 - Oi) tileAlpha

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Manipulating Points

• ss2 ss sTranslatett2 tt tTranslate
• ss3 ss2 cos(angle) - tt2
  sin(angle)tt3 ss2 sin(angle) tt2
  cos(angle)
• ss4 ss3 sScalett4 tt3 tScale

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Manipulating Points

• ss2 ss sTranslatett2 tt tTranslate
• ss3 ss2 cos(angle) - tt2
  sin(angle)tt3 ss2 sin(angle) tt2
  cos(angle)
• ss4 ss3 sScalett4 tt3 tScale

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Manipulating Points

• ss2 ss sTranslatett2 tt tTranslate
• ss3 ss2 cos(angle) - tt2
  sin(angle)tt3 ss2 sin(angle) tt2
  cos(angle)
• ss4 ss3 sScalett4 tt3 tScale

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Manipulating Points

• ss2 ss sTranslatett2 tt tTranslate
• ss3 ss2 cos(angle) - tt2
  sin(angle)tt3 ss2 sin(angle) tt2
  cos(angle)
• ss4 ss3 sScalett4 tt3 tScale

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Point Sampling

• texture(tex, ss, tt, "swidth?, 0, "twidth?,
  0)
• texture(tex, ss, tt, ss, tt, ss, tt, ss,
  tt)

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Point Sampling

• texture(tex, ss, tt, "swidth", 0, "twidth",
  0)
• texture(tex, ss, tt, ss, tt, ss, tt, ss,
  tt)

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The End