Volume Rendering, pt 1. Hank Childs, University of Oregon

Transcription

1 Volume Rendering, pt 1 Hank Childs, University of Oregon

2 Announcements No class Friday Grad students: No project 8G s8ll need to do short presenta8ons Come to OH and let s chat

3 Plo$ng Techniques X- rays Film/image EmiAer

4 Volume rendering Important visualiza8on technique for 3D data Use combina8on of color and transparency to see en8re 3D data set at one 8me. There are mul8ple ways to do volume rendering. I will describe one way today (raycas8ng). That will help explain the technique. I will describe alternate ways in future lectures.

5 Volume rendering overview Camera Pixels on the screen 3D data

6 Volume rendering overview Camera Pixels on the screen Ray cas8ng game plan: For every pixel on the screen, 3D data Find ray for that pixel Intersect volume with ray Calculate color from intersec8on Which of these 4 steps will be easy? Which will be hard? Assign color to pixel

7 Outline Find Ray For That Pixel Intersect Volume With Ray Calculate Color From Intersec8on Assign Color To Pixel

8 Outline Find Ray For That Pixel Intersect Volume With Ray Calculate Color From Intersec8on Assign Color To Pixel

9 How do we specify a camera? The viewing pyramid or view frustum. Frustum: In geometry, a frustum (plural: frusta or frustums) is the por8on of a solid (normally a cone or pyramid) that lies between two parallel planes cu\ng it.

10 NOT doing it the graphics way (yet) O O World space: Triangles in na8ve Cartesian coordinates Camera located anywhere Camera space: Camera located at origin, looking down - Z Triangle coordinates rela8ve to camera frame z y x Image space: All viewable objects within - 1 <= x,y,z <= +1 Screen space: All viewable objects within - 1 <= x, y <= +1 Device space: All viewable objects within 0<=x<=width, 0 <=y<=height We don t need to do it this way for volume rendering (although we could)

11 From Pixels to Rays r u r v = = look up look up r look u r look u r Δ x = r Δ y = 2 tan( fovx / 2) r u W 2 tan( fovy / 2) r v H From: Zhang, CSUSM, Introduc8on to Ray Tracing r look (2i + 1 W) r (2 j + 1 H) r di (, j) = + Δ x+ Δy look 2 2 This answers the find ray for this pixel ques8on

12 Outline Find Ray For That Pixel Intersect Volume With Ray Calculate Color From Intersec8on Assign Color To Pixel

13 Intersect Volume With Ray Camera Pixels on the screen } 3D data What is the result of the ray- volume intersec8on?

14 Ray- Volume Intersec8on How would you calculate this intersec8on?

15 Ray- Volume Intersec8on: How do you do it? Find first cell intersected Intersec8on is at a face Find where ray exits that cell That face is shared with another cell Keep going un8l you exit the volume, one cell at a 8me. What would this technique give you?

16 Intersect Volume With Ray Pixels on the screen } Camera 3D data What data would we be working with?

17 Face Intersec8ons Can we calculate the intersec8ons at the faces? Can we calculate the data at the faces? X Is this a good idea? Why or why not? (it is not a good idea if we interpolate between the face values) How do we fix this? X

18 Ray- Volume Intersec8on: sampling Camera x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Pixels on the screen 3D data Sampling is the most common method for ray- cas8ng volume rendering Do we know how to do this sampling?

19 How to sample quickly Mul8ple strategies. For now, similar as before: Find first cell intersected Intersec8on is at a face Find where ray exits that cell Are there samples within the cell? Then sample them? Go to next cell (which shares a face) and repeat Keep going un8l you exit the volume, one cell at a 8me, and see what samples it covers Approximately how many samples will we calculate?

20 Outline Find Ray For That Pixel Intersect Volume With Ray Calculate Color From Intersec8on Assign Color To Pixel

21 Refresher: Color Maps

22 Transfer func8on Assigns a color and an opacity to each scalar value. Technique Pseudocoloring Volume Rendering Abstrac5on for assigning color Color Map Transfer Func8on

23 Transfer Func8on

24 Applying a transfer func8on Sample Scalar Value R G B A Quiz: calculate (approximate) results from transfer func8on for each sample

25 Transparency Quiz: If you have a red square that is 50% opaque in front of a black background, what color would you see? Represent your answer in terms of (R, G, B) Answer: (128, 0, 0)

26 Transparency If you have an opaque red square in front of a blue square, what color would you see? Red If you have a 50% transparent red square in front of a blue square, what color would you see? Purple If you have a 100% transparent red square in front of a blue square, what color would you see? Blue

27 Formula For Transparency Front = (Fr,Fg,Fb,Fa) a = alpha, transparency factor Some8mes percent Typically 0-255, with 255 = 100%, 0 = 0% Back = (Br,Bg,Bb,Ba) Equa8on = (Or = Fa*Fr+(1- Fa)*Ba*Br, Og = Fa*Fg+(1- Fa)*Ba*Bg, Ob = Fa*Fb+(1- Fa)*Ba*Bb, Oa = Fa+(1- Fa)*Ba) Alpha component is important! Any observa8ons?

28 Represen8ng Colors Two ways of represen8ng colors Pre- mul8plica8on Straight RGBA (non- premul8plied) Slides use straight RGBA Wikipedia page is great reference: hap://en.wikipedia.org/wiki/alpha_composi8ng

29 Represen8ng colors: example 50% transparent red square Could use (128, 0, 0, 0.5) # pre- mul8plied - - or- - (255, 0, 0, 0.5) # straight RGBA The issue is whether the 0.5 is mul8plied into the color components first. And changes equa8on

30 Formula For Transparency Front = (Fr,Fg,Fb,Fa) a = alpha, transparency factor Some8mes percent Typically 0-255, with 255 = 100%, 0 = 0% Back = (Br,Bg,Bb,Ba) Equa8on = (Or = Fa*Fr+(1- Fa)*Ba*Br, Og = Fa*Fg+(1- Fa)*Ba*Bg, Ob = Fa*Fb+(1- Fa)*Ba*Bb, Oa = Fa+(1- Fa)*Ba) Formula for straight RGBA Alpha component is important! Any observa8ons?

31 Formula For Transparency Front = (Fr,Fg,Fb,Fa) a = alpha, transparency factor Some8mes percent Typically 0-255, with 255 = 100%, 0 = 0% Back = (Br,Bg,Bb,Ba) Equa8on = (Or = Fr+(1- Fa)*Ba*Br, Og = Fg+(1- Fa)*Ba*Bg, Ob = Fb+(1- Fa)*Ba*Bb, Oa = Fa+(1- Fa)*Ba) Formula for pre- mul8plied Alpha component is important! Any observa8ons?

32 Transparency If you have an 25% transparent red square (255,0,0) in front of a blue square (0,0,255), what color would you see (in RGB)? (192,0,64) If you have an 25% transparent blue square (0,0,255) in front of a red square (255,0,0), what color would you see (in RGB)? (64,0,192)

33 Calcula8ng Color Sample Scalar Value R G B A Equa8on = (Fa*Fr+(1- Fa)*Ba*Br, Fa*Fg+(1- Fa)*Ba*Bg, Fa*Fb+(1- Fa)*Ba*Bb, Fa+(1- Fa)*Ba) Apply this equa8on over and over un8l you run out of samples (then use background color)

34 Game Plan Ini8alize pixel color / alpha with TransferFunc8on(first sample) Iterate over remaining samples Front- to- back order pixel color / alpha updated each 8me using composite func8on

35 Outline Find Ray For That Pixel Intersect Volume With Ray Calculate Color From Intersec8on Assign Color To Pixel

36 Assign Color To Pixel Allocate a buffer for storing RGB values Buffer should have one RGB for every pixel on the screen. As you calculate color for a ray, assign that color to its corresponding buffer entry When you have all of the colors, put that image up on the screen, as if you had rendered it using graphics cards.

37 Volume rendering overview Camera Pixels on the screen Ray cas8ng game plan: For every pixel on the screen, 3D data Find ray for that pixel Intersect volume with ray Calculate color from intersec8on Which of these 4 steps were easy? Which were hard? Assign color to pixel

38 Next Time A lot more about volume rendering More techniques Mul8- variate volume rendering Ligh8ng calcula8ons Op8miza8ons Combina8ons with surface rendering