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Rasterization CS 148: Summer 2016 Introduction of Graphics and - - PowerPoint PPT Presentation

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Rasterization CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain http://iloveshaders.blogspot.com/2011/05/how-rasterization-process-works.html Render [ren-der]: The process of generating an image from a description of a

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CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain

Rasterization

http://iloveshaders.blogspot.com/2011/05/how-rasterization-process-works.html

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Render [ren-der]:

The process of generating an image from a description

  • f a scene by means of a computer program

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 2

https://en.wikipedia.org/wiki/Rendering_(computer_graphics)

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Two Ways to Render an Image

3 CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain

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Two Ways to Render an Image

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 4

Projection: 3D description to 2D description

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Two Ways to Render an Image

Rasterization

http://iloveshaders.blogspot.com/2011/05/how-rasterization-process-works.html

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 5

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Two Ways to Render an Image

http://upload.wikimedia.org/wikipedia/commons/8/83/Ray_trace_diagram.svg CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 6

Raytracing

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Rasterization

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 7

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Rasterize [rastərʌɪz]:

To convert vector data to raster format.

Rasterize [rastərʌɪz]:

To convert vector data to raster – pixel or dot – format.

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 8

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Rasterization Process

“A triangle is here, a circle is there, …” “This pixel is yellow…”

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 9

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Scan Conversion

Figuring out which pixels to shade.

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 10

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The Basics: Framebuffer

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 11

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The Basics: Framebuffer

Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel Pixel

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 12

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Framebuffer Coordinates

(0,0)

+ x

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 13

Pixel Center

+ y

(1,1) (2,1)

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Problem

+ x + y

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 14

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The Basics: Scan Conversion

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 15

+ x + y

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The Basics: Scan Conversion

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 16

+ x + y

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Convention

+ x + y

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 17

Must intersect diamond

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Convention

+ x + y

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 18

Must intersect diamond

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Desirable Properties

  • Fast
  • Simple
  • Integer arithmetic

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 19

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Bresenham’s Algorithm

  • Introduced in 1967
  • Best-fit approximation

under some conditions

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 20

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Bresenham’s Algorithm

  • Introduced in 1967
  • Best-fit approximation

under some conditions

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 21

Variation by Pitteway (1967) “Midpoint Algorithm”

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Bresenham’s Algorithm

  • Equation of a line

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 22

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Bresenham’s Algorithm

  • Equation of a line

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 23

Assumption:

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Bresenham’s Algorithm

  • Equation of a line

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 24

Assumption:

Easy fix via rotation/reflection

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 25

1 𝜗 Stategy

  • Every step: increment x
  • Keep track of “error” ϵ
  • At every step accumulate
  • 𝜗 ← 𝜗 + 𝑛
  • If 𝜗 ≥

' (

  • Increment y
  • Reset 𝜗 ← 𝜗 + 𝑛 − 1
  • Start with 𝜗 = 𝑛
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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 26

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 + 𝒏 − 𝟐 else 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 1

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 27

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 + 𝒏 − 𝟐 else 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 1

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 28

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 1

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 29

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 (𝑦0,𝑧0) 𝑦,𝑧

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 30

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 (𝑦0,𝑧0) 𝑦,𝑧

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 31

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 (𝑦0,𝑧0) 𝑦,𝑧

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 32

Algorithm

line(𝒚𝟏, 𝒛𝟏,𝒚𝟐, 𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 > 𝟐

𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 (𝑦0,𝑧0) 𝑦,𝑧

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 33

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 >

𝟐 𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 34

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝝑 = 𝒏 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 >

𝟐 𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 = 𝑛 =

=> =?

⇒ Δ𝑦 𝜗 = Δ𝑧 ⇒ 2Δ𝑦 𝜗 = 2Δ𝑧 Use 𝑒 = 2Δ𝑦 𝜗

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 35

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 >

𝟐 𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 = 𝑛 =

=> =?

⇒ Δ𝑦 𝜗 = Δ𝑧 ⇒ 2Δ𝑦 𝜗 = 2Δ𝑧 Use 𝑒 = 2Δ𝑦 𝜗

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 36

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝝑 >

𝟐 𝟑

𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 37

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 38

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝝑 ← 𝝑 − 𝟐 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 39

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝒆 ← 𝒆 − 𝟑𝚬𝐲 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 40

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝒆 ← 𝒆 − 𝟑𝚬𝐲 𝝑 ← 𝝑 + 𝒏 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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SLIDE 41

Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 41

line(𝒚𝟏, 𝒛𝟏, 𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝒆 = 𝟑𝚬𝐳 while 𝒚 < 𝒚𝟐 pixel(𝒚, 𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝒆 ← 𝒆 − 𝟑𝚬𝐲 𝒆 ← 𝒆 + 𝟑𝚬𝐳 𝒚 ← 𝒚 + 𝟐

𝜗 >

' (

⇒ 2Δ𝑦 𝜗 > Δx ⇒ 𝑒 > Δ𝑦

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Bresenham’s Algorithm

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 42

line(𝒚𝟏,𝒛𝟏,𝒚𝟐,𝒛𝟐) 𝒚 ← 𝒚𝟏 𝐳 ← 𝒛𝟏 𝚬y ← 𝒛𝟐 − 𝒛𝟏 𝚬𝒚 ← 𝒚𝟐 − 𝒚𝟏 twoDY ← 𝚬𝐳 ≪ 𝟐 twoDX ← 𝚬𝐲 ≪ 𝟐 𝒆 = twoDY while 𝒚 < 𝒚𝟐 pixel(𝒚,𝒛) if 𝒆 > 𝚬𝐲 𝒛 ← 𝒛 + 𝟐 𝒆 ← 𝒆 −twoDX 𝒆 ← 𝒆 +twoDY 𝒚 ← 𝒚 + 𝟐

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Different Method: Same Output

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 43

Pitteway (1967) “Midpoint Algorithm” READING ASSIGNMENT !

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Rasterizing Circle

+ x + y

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 44

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 45

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 46

Equation of a line:

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 47

Equation of a line: Implicit Form

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 48

Equation of a line: Implicit Form

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 49

F(x, y) > 0

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 50

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 51

Assume

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Midpoint Algorithm: Idea

Assume

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 52

NE E

Choose between E and NE

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 53

Decision variable: for next move NE E

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 54

Decision variable: for next move In this case NE E

Choose NE

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 55

Decision variable update When NE was chosen

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 56

Decision variable update When NE was chosen If E were chosen instead

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 57

Recall

Fraction!

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Midpoint Algorithm: Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 58

Recall

Fraction! Define Implicit Function as:

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Midpoint Algorithm: Summary

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 59

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Circle with Midpoint Algorithm

+ x + y

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 60

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Important Issues We’ve Ignored

http://www.cheap-computermonitors.com/images/1-cheap-flat-screen-computer-monitors.jpg

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 61

Clipping

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 62

Clipping

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 63

Clipping

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Important Issues We’ve Ignored

Line intensity

l ¼ 7:07 p = 5 l = 5 p = 5

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 64

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 65

Line Thickness

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 66

Antialiasing

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 67

Antialiasing

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 68

Antialiasing

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Important Issues We’ve Ignored

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 69

Stippling Patterns

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Filling Triangles

  • Optimize a single primitive
  • Nice properties:
  • Planar
  • “Inside” well-defined
  • Straightforward shading

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 70

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Have We Lost Anything?

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 71

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Have We Lost Anything?

Non-convex!

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 72

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SLIDE 73

Have We Lost Anything?

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CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 73

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SLIDE 74

Two Methods for Filling

Check if each pixel in bounding box is inside the triangle. Rasterize border; sweep from left to right.

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 74

Parallelizable Less Computation

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SLIDE 75

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 75

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SLIDE 76

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 76

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SLIDE 77

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 77

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SLIDE 78

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 78

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SLIDE 79

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 79

Point inside

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SLIDE 80

Barycentric Coordinates

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 80

Point outside

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SLIDE 81

Barycentric Interpolation

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SLIDE 82

Barycentric Interpolation

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SLIDE 83

Barycentric Interpolation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 83

Linear

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SLIDE 84

Barycentric Interpolation

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Continuous across boundaries

Only depends on these two

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SLIDE 85

Issues

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Adjacency and Singularity

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SLIDE 86

More Issues

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Small triangle and slivers

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SLIDE 87

CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain

Rasterization

http://iloveshaders.blogspot.com/2011/05/how-rasterization-process-works.html