ACS BIOT Call For Papers
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English

ACS BIOT Call For Papers

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  • cours - matière : chemical
  • exposé
ACS BIOT Call For Papers  2010  American Chemical Society - Biochemical Technology (BIOT) Division 239th - ACS National Meeting & Exposition March 21-25, 2010 – San Francisco, CA Program Chairs: Claire Komives & David Roush CALL FOR PAPERS I. Upstream Processes Advances in Biocatalysis .............................................................................................................. 3 Advances in Microbial and Algal Fermentation Process Development.........................................3 Advances in Metabolic Engineering..............................................................................................3 Advances in Cell Culture Process Development – Cellular .......................................................... 4 Advances in Cell Culture Process Development – Reactors .......................................................4 Protein Expression and Post-Translational Modification............................................................... 5 Advances in Systems Biology....................................................................................................... 5 II.
  • selection of novel excipients
  • protein expression
  • production of aggregates
  • cell culture process development
  • metabolic engineering
  • drug delivery
  • techniques
  • technologies
  • development
  • cell

Subjects

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Language English

Computer Graphics

- Rasterization & Clipping -
Philipp Slusallek Overview
• Last lecture:
– Camera transformations
– Projection

• Today:
– Rasterization of lines and triangles
– Clipping

• Next lecture:
– OpenGL Rasterization
• Definition
– Given some geometry (point, 2D line, circle, triangle, polygon,…),
specify which pixels of a raster display each primitive covers
• Often also called “scan-conversion”
– Anti-aliasing: instead of only fully-covered pixels (single sample),
specify what part of a pixel is covered (super-sampling)
• Perspectives
– OpenGL lecture: from an application programmer’s point of view
– This lecture: from a graphics package implementer’s point of view
• Usages of rasterization in practice
– 2D-raster graphics, e.g. Postscript
– 3D-raster graphics
– 3D volume modeling and rendering
– Volume operations (CSG operations, collision detection)
– Space subdivision (spatial index structures): construction and
traversal Rasterization
• Assumptions y
– Pixels are sample points on a 2D integer grid
• OpenGL: cell bottom-left integer-coordinate
x • X11, Foley: at the cell center (we will use this)
– Simple raster operations
• Just setting pixel values or not (binary decision)
• More complex operations later: compositing/anti-aliasing
– Endpoints snapped to (sub-)pixel coordinates
• Simple and consistent computations with fixed-point arithmetic
– Limiting to lines with gradient/slope |m|  1 (mostly horizontal)
• Separate handling of horizontal and vertical lines
• For mostly vertical, swap x and y (|1/m|  1), rasterize, swap back
– Line size is one pixel
• |m|  1: 1 pixel per column (X-driving axis)
• |m| > 1: 1 pixel per row (Y-driving axis) �

















Lines: As Functions
• Specification
– Initial and end points: ( , ),( , ),(�� ,�� )= ( − , − ) 00 0
– Functional form: = +
– End points with integer coordinates  rational slope = /��
• Goal
– Find pixels whose distance to the line is smallest
• Brute-force algorithm
– Assume that +X is the driving axis, so set pixel in every column
for x = x to xi 0 e
y = m * x + B i i
setPixel(x , Round(y )) // Round(y ) = Floor(y + 0.5) i i i i
• Comments
– Variables m and y are originally calculated in floating-point i
– Not well suited for direct HW implementation
��Lines: DDA
• DDA: Digital Differential Analyzer
– Origin of incremental solvers for simple differential equations
• The Euler method
– Per time-step: x’ = x + dx/dt, y’ = y + dy /dt
• Incremental algorithm
– Choose dt=dx, then per pixel
• x = x + 1 i+1 i
• y = m * x + B = m(x + 1) + B = (m * x + B) + m = y + m i+1 i+1 i i i
• setPixel(x , Round(y )) i+1 i+1
• Remark
– Utilization of line coherence through incremental calculation
• Avoid the “costly” multiplication – less important today
– Accumulates error over length of the line
• Up to 2k adds on HD!
– Floating point calculations may be moved to fixed point
• Must control accuracy of fixed point representation
• Enough extra bits to hide accumulated error (~11 bits for HD) �

��

���

























��

Lines: Bresenham (1963)
• DDA analysis
– Critical point: decision by rounding up or down
• Idea
– Integer-based decision through implicit functions
– Implicit line equation
• , = �� +�� + = 0
��
– Here with = �� + = + ⇒ 0=�� −�� + ��
��
• = , = − , =
– Results in
• , = − + = 0
, = 0

( , ) < 0
, > 0
�� �� ���
















Lines: Bresenham
• Decision variable d (the midpoint formulation)
– Assume we are at x=i, calculating next step at x=i+1
– Measures the vertical distance of midpoint from line:
= = +1, +1 2 +1 +1
= +1 + +1 2 +
Mi+1
• Preparations for the next pixel
i i+1 IF (d  0) // Increment in x only i+1
d = d + a = d + dy // Incremental calculation i+2 i+1 i+1
ELSE // Increment in x and y
d = d + a + b = d + dy – dx i+2 i+1 i+1
y = y + 1
ENDIF
x = x + 1 �






��








���



















Lines: Integer Bresenham
• Initialization
1 1
= +1, + = +1 + + + 1 0 0 0 02 2–
= + + + + = , + + = +0 0 0 02 2 2
– Because F( , ) is zero by definition (line goes through (x , y )) 0 0 0 0
• Pixel is always set (but check consistency rules → later)
• Elimination of fractions
– Any positive scale factor maintains the sign of F(x,y)
• 2� , = 2 + + → = 2� + 0 0 0 0
• Observation:
– When the start and end points have integer coordinates then
b = -dx and a = dy have also integer values
• Floating point computation can be eliminated
– No accumulated error Lines: Arbitrary Directions
• 8 different cases
– Driving (active) axis: ±X or ±Y
– Increment/decrement of y or x, respectively

+Y,x-- +Y,x++
-X,y++ +X,y++
-X,y-- +X,y--
-Y,x-- -Y,x++

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