with Polynomial Filters Josiah Manson and Scott Schaefer Texas - - PowerPoint PPT Presentation

▶
with polynomial filters
SMART_READER_LITE
LIVE PREVIEW

with Polynomial Filters Josiah Manson and Scott Schaefer Texas - - PowerPoint PPT Presentation

Jan 22, 2024 268 likes •976 views

Analytic Rasterization of Curves with Polynomial Filters Josiah Manson and Scott Schaefer Texas A&M University Motivation Motivation Motivation Motivation Motivation Motivation Motivation Constant colors Color gradients Motivation

slide-1
SLIDE 1

Analytic Rasterization of Curves with Polynomial Filters

Josiah Manson and Scott Schaefer Texas A&M University

slide-2
SLIDE 2

Motivation

slide-3
SLIDE 3

Motivation

slide-4
SLIDE 4

Motivation

slide-5
SLIDE 5

Motivation

slide-6
SLIDE 6

Motivation

slide-7
SLIDE 7

Motivation

slide-8
SLIDE 8

Motivation

Constant colors Color gradients

slide-9
SLIDE 9

Motivation

slide-10
SLIDE 10

Input

Curve Boundary Piecewise Filter

slide-11
SLIDE 11

Input

Curve Boundary Piecewise Filter

[Manson and Schaefer, 2011] “Wavelet Rasterization” [Duff, 1989] “Polygon scan conversion by exact convolution”

slide-12
SLIDE 12

Signal Sampling

slide-13
SLIDE 13

Signal Sampling

slide-14
SLIDE 14

Signal Sampling

slide-15
SLIDE 15

Signal Sampling

slide-16
SLIDE 16

Signal Sampling

slide-17
SLIDE 17

Signal Sampling

slide-18
SLIDE 18

Image Sampling

Image

slide-19
SLIDE 19

Image Sampling

Pixel positions

slide-20
SLIDE 20

Image Sampling

Evaluate at point

slide-21
SLIDE 21

Image Sampling

Center filter at point

slide-22
SLIDE 22

Image Sampling

Center filter at point

slide-23
SLIDE 23

Image Sampling

Center filter at point

slide-24
SLIDE 24

Image Sampling

Multiply

slide-25
SLIDE 25

Image Sampling

Integrate

slide-26
SLIDE 26

Image Sampling

Repeat for all pixels

slide-27
SLIDE 27

Derivation

slide-28
SLIDE 28

Derivation

slide-29
SLIDE 29

Derivation

slide-30
SLIDE 30

Derivation

slide-31
SLIDE 31

Derivation

slide-32
SLIDE 32

Derivation

slide-33
SLIDE 33

Derivation

slide-34
SLIDE 34

Derivation

slide-35
SLIDE 35

Filter Integrals

slide-36
SLIDE 36

Constant Zero Zero

Filter Integrals

Zero C h a n g e s C h a n g e s

slide-37
SLIDE 37

Filter Pieces

slide-38
SLIDE 38

Scanline Rasterization

slide-39
SLIDE 39

Scanline Rasterization

slide-40
SLIDE 40

Scanline Rasterization

slide-41
SLIDE 41

Scanline Rasterization

Changing

slide-42
SLIDE 42

Scanline Rasterization

Constant Changing

slide-43
SLIDE 43

Scanline Rasterization

slide-44
SLIDE 44

Scanline Rasterization

slide-45
SLIDE 45

Scanline Rasterization

slide-46
SLIDE 46

Scanline Rasterization

slide-47
SLIDE 47

Scanline Rasterization

+

slide-48
SLIDE 48

Scanline Rasterization

slide-49
SLIDE 49

Scanline Rasterization

slide-50
SLIDE 50

Scanline Rasterization

+

slide-51
SLIDE 51

Scanline Rasterization

slide-52
SLIDE 52

Scanline Rasterization

slide-53
SLIDE 53

Scanline Rasterization

+

slide-54
SLIDE 54

Scanline Rasterization

slide-55
SLIDE 55

Scanline Rasterization

slide-56
SLIDE 56

Scanline Rasterization

+

slide-57
SLIDE 57

Scanline Rasterization

slide-58
SLIDE 58

Scanline Rasterization

slide-59
SLIDE 59

Filter Pieces

= +

slide-60
SLIDE 60

Filter Pieces

+ =

slide-61
SLIDE 61

Rational Curves

slide-62
SLIDE 62

Cubic Curves

Input image Mitchell-Netravali

slide-63
SLIDE 63

Anti-aliasing

Point sampling 16x MSAA tent Analytic tent ATI Radeon HD 5700

slide-64
SLIDE 64

Anti-aliasing

Box

slide-65
SLIDE 65

Anti-aliasing

Tent

slide-66
SLIDE 66

Anti-aliasing

Lanczos 3

slide-67
SLIDE 67

Anti-aliasing

Radial 3

slide-68
SLIDE 68

Timings (ms)

slide-69
SLIDE 69

Parallelism

slide-70
SLIDE 70

Conclusions

  • Analytic prefiltering

– Smooth curves – High-quality filters – Color gradients

  • Fast algorithm

– Independent curves and filter pieces – High parallelism