1. Projections and Picking Wed 24 Sep 2003
project 1 solution demo
recap: projections 2
projections 3
picking

2. News Project 1 solution executable available Readings reminder
idea of what’s expected
no need to copy look and feel exactly
Readings reminder
Chapter 5
Week 4, Wed 24 Sep 03
© Tamara Munzner

3. Projections recap

4. Transforming View Volumes
orthographic view volume x z
VCS y
x=left
y=top
x=right
z=-far
z=-near
y=bottom
perspective view volume
NDCS y
(1,1,1) z
(-1,-1,-1) x
Week 4, Wed 24 Sep 03
© Tamara Munzner

5. Basic Perspective Projectiony
P(x,y,z)
similar triangles
P(x’,y’,d) z
z=d
also
but
nonuniform foreshortening
not affine
Week 4, Wed 24 Sep 03
© Tamara Munzner

6. Basic Perspective Projection
can express as homogenous 4x4 matrix!
Week 4, Wed 24 Sep 03
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7. Projective Transformations
determining the matrix representation
need to observe 5 points in general position, e.g.
[left,0,0,1]T[-1,0,0,1]T
[0,top,0,1]T[0,1,0,1]T
[0,0,-f,1]T[0,0,1,1]T
[0,0,-n,1]T[0,0,-1,1]T
[left*f/n,top*f/n,-f,1]T[-1,1,1,1]T
solve resulting equation system to obtain matrix
Week 4, Wed 24 Sep 03
© Tamara Munzner

8. OpenGL Orthographic Matrix
scale, translate, reflect for new coord sys
Week 4, Wed 24 Sep 03
© Tamara Munzner

9. OpenGL Perspective Matrix
shear, scale, reflect for new coord sys
Week 4, Wed 24 Sep 03
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10. Projection Normalization
viewing
clipping
normalized
device
VCS
CCS
NDCS
projection
transformation
perspective
division
alter w
/ w
distort such that orthographic projection of distorted objects is desired persp projection
separate division from standard matrix multiplies
division: normalization
Week 4, Wed 24 Sep 03
© Tamara Munzner

11. Projections 3

12. Demos Brown Projections Demos
Nate Robbins tutorial (take 2):
Week 4, Wed 24 Sep 03
© Tamara Munzner

13. Perspective Example view volume left = -1, right = 1 bot = -1, top = 1
near = 1, far = 4
Week 4, Wed 24 Sep 03
© Tamara Munzner

14. Perspective Example view volume left = -1, right = 1 tracks in VCS:
bot = -1, top = 1
near = 1, far = 4
tracks in VCS:
left x=-1, y=-1
right x=1, y=-1
x=-1
x=1 1
ymax-1
z=-4
real midpoint
z=-1 -1 -1 1
xmax-1 x -1
NDCS
(z not shown)
DCS
(z not shown) z
VCS top view
Week 4, Wed 24 Sep 03
© Tamara Munzner

15. Perspective Example
/ w
Week 4, Wed 24 Sep 03
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16. Viewport Transformation
generate pixel coordinates
map x, y from range –1…1 (normalized device coordinates) to pixel coordinates on the display
involves 2D scaling and translation y
display x
viewport
Week 4, Wed 24 Sep 03
© Tamara Munzner

17. Viewport Transformation
(1,1)
(w,h)
DCS b
NDCS a y
(-1,-1) x
(0,0)
OpenGL
glViewport(x,y,a,b);
default:
glViewport(0,0,w,h);
Week 4, Wed 24 Sep 03
© Tamara Munzner

18. Projective Rendering Pipeline
glVertex3f(x,y,z)
object
world
viewing
alter w
OCS
WCS
VCS
glFrustum(...)
projection
transformation
modeling
transformation
viewing
transformation
clipping
glTranslatef(x,y,z)
glRotatef(th,x,y,z)
....
gluLookAt(...)
/ w
CCS
perspective
division
normalized
device
OCS - object coordinate system
WCS - world coordinate system
VCS - viewing coordinate system
CCS - clipping coordinate system
NDCS - normalized device coordinate system
DCS - device coordinate system
glutInitWindowSize(w,h)
glViewport(x,y,a,b)
NDCS
viewport
transformation
device
DCS
Week 4, Wed 24 Sep 03
© Tamara Munzner

19. Picking

20. Interactive Object Selection
move cursor over object, click
how to decide what is below?
ambiguity
many 3D world objects map to same 2D point
four common approaches
manual ray intersection
bounding extents
backbuffer color coding
selection region with hit list
Picking and 3D Selection
Pick: Select an object by positioning mouse over it and clicking.
Question: How do we decide what was picked?
We could do the work ourselves:
Map selection point to a ray;
Intersect with all objects in scene.
Let OpenGL/graphics hardware do the work.
Idea: Draw entire scene, and ``pick'' anything drawn near the cursor.
Only ``draw'' in a small viewport near the cursor.
Just do clipping, no shading or rasterization.
Need a method of identifying ``hits''.
OpenGL uses a name stack managed by glInitNames(), glLoadName(), glPushName(), and glPopName().
``Names'' are unsigned integers
When hit occurs, copy entire contents of stack to output buffer.
Process:
Set up pick buffer
Initialize name stack May need pushName(-1);
Save old projective transformation and set up a new one
Draw your scene with appropriate use of name stack
Restore projective transformation
Query for number of hits and process them
A hit occurs if a draw occurs in the (small) viewport
All information (except 'hits') is stored in buffer given with glSelectBuffer
Example:
Two objects
Might pick none
Might pick either one
Might pick both
glSelectBuffer(size, buffer); /* initialize */ glRenderMode(GL_SELECT); glInitNames(); glPushName(-1); glGetIntegerv(GL_VIEWPORT,viewport); /* set up pick view */ glMatrixMode(GL_PROJECTION); glPushMatrix(); glIdentity(); gluPickMatrix(x,y,w,h,viewport); glMatrixMode(GL_MODELVIEW); ViewMatrix(); glLoadName(1); Draw1(); glLoadName(2); Draw2(); glMatrixMode(GL_PROJECTION); glPopMatrix(); glMatrixMode(GL_MODELVIEW); hits = glRenderMode(GL_RENDER);
Hits stored consequetively in array
In general, if h is the number of hits, the following is returned.
hits = h.
h hit records, each with four parts:
The number of items q on the name stack at the time of the hit (1 int).
The minimum z value amoung the primitives hit (1 int).
The maximum z value amoung the primitives hit (1 int).
The contents of the hit stack, deepest element first (q ints).
At most one hit between each call glRenderMode or a change to name stack
In our example, you get back the following:
If you click on Item 1 only: hits = 1, buffer = 1, min(z1), max(z1), 1.
If you click on Item 2 only: hits = 1, buffer = 1, min(z2), max(z2), 2.
If you click over both Item 1 and Item 2: hits = 2, buffer = 1, min(z1), max(z1), 1, 1, min(z2), max(z2), 2.
More complex example: /* initialization stuff goes here */ glPushName(1); Draw1(); /* stack: 1 */ glPushName(1); Draw1_1(); /* stack: 1 1 */ glPushName(1); Draw1_1_1(); /* stack: */ glPopName(); glPushName(2); Draw1_1_2(); /* stack: */ glPopName(); glPopName(); glPushName(2); /* stack: 1 2 */ Draw1_2(); glPopName(); glPopName(); glPushName(2); Draw2(); /* stack: 2 */ glPopName(); /* wrap-up stuff here */
What you get back:
If you click on Item 1: hits = 1, buffer = 1, min(z1), max(z1), 1.
If you click on Items 1:1:1 and 1:2: hits = 2, buffer = 3, min(z111), max(z111), 1, 1, 1, 2, min(z12), max(z12), 1, 2.
If you click on Items 1:1:2, 1:2, and 2: hits = 3, buffer = 3, min(z112), max(z112), 1, 1, 2, 2, min(z12), max(z12), 1, 2, 1, min(z2), max(z2), 2.
Important Details:
Make sure that projection matrix is saved with a glPushMatrix() and restored with a glPopMatrix().
glRenderMode(GL_RENDER) returns negative if buffer not big enough.
When a hit occurs, a flag is set.
Entry to name stack only made at next gl*Name(s) or glRenderMode call. So, each draw block can only generate at most one hit.
Readings: GL Programming Manual, Chapter 12
The user provides each object of interest with a “name” (in fact, the name is an integer).
The user defines a small region of the screen. Typically, this is a rectangle that includes
the mouse position and a few pixels either side.
OpenGL then renders the scene in selection mode. Whenever a named object is displayed
inside the selected region, a “hit record”, containing its name and some other information
is added to the “selection list”.
The user examines the hit records to determine the object — or objects — selected.
Week 4, Wed 24 Sep 03
© Tamara Munzner

21. Manual Ray Intersection
do all computation at application level
map selection point to a ray
intersect ray with all objects in scene.
advantages
no library dependence y
VCS x
Week 4, Wed 24 Sep 03
© Tamara Munzner

22. Manual Ray Intersection
do all computation at application level
map selection point to a ray
intersect ray with all objects in scene.
advantages
no library dependence
disadvantages
difficult to program
slow: work to do depends on total number and complexity of objects in scene
Week 4, Wed 24 Sep 03
© Tamara Munzner

23. Bounding Extents keep track of axis-aligned bounding rectangles
advantages
conceptually simple
easy to keep track of boxes in world space
Week 4, Wed 24 Sep 03
© Tamara Munzner

24. Bounding Extents disadvantages extensions low precision
must keep track of object-rectangle relationship
extensions
do more sophisticated bound bookkeeping
Week 4, Wed 24 Sep 03
© Tamara Munzner

25. Backbuffer Color Coding
use backbuffer for picking
create image as computational entity
never displayed to user
redraw all objects in backbuffer
turn off shading calculations
set unique color for each pickable object
store in table
read back pixel at cursor location
check against table
Week 4, Wed 24 Sep 03
© Tamara Munzner

26. Backbuffer Color Coding
advantages
conceptually simple
variable precision
disadvantages
number of color bits must be adequate
introduce 2x redraw delay
Week 4, Wed 24 Sep 03
© Tamara Munzner

27. Backbuffer Example
for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) { glPushMatrix(); switch (i*2+j) { case 0: glColor3ub(255,0,0);break; case 1: glColor3ub(0,255,0);break; case 2: glColor3ub(0,0,255);break; case 3: glColor3ub(250,0,250);break; } glTranslatef(i*3.0,0,-j * 3.0) glCallList(snowman_display_list); glPopMatrix(); }
glColor3f(1.0f, 1.0f, 1.0f);
for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) { glPushMatrix(); glTranslatef(i*3.0,0,-j * 3.0); glColor3f(1.0f, 1.0f, 1.0f); glCallList(snowman_display_list); glPopMatrix(); }
Week 4, Wed 24 Sep 03
© Tamara Munzner

28. Select/Hit use small region around cursor for viewport
assign per-object integer keys (names)
redraw in special mode
store hit list of objects in region
examine hit list
OpenGL support
Week 4, Wed 24 Sep 03
© Tamara Munzner

29. Viewport small rectangle around cursor why rectangle instead of point?
change coord sys so fills viewport
why rectangle instead of point?
people aren’t great at positioning mouse
Fitts’s Law: time to acquire a target is function of the distance to and size of the target
allow several pixels of slop
Week 4, Wed 24 Sep 03
© Tamara Munzner

30. Viewport tricky to compute simple utility command
invert viewport matrix, set up new orthogonal projection
simple utility command
gluPickMatrix(x,y,w,h,viewport)
x,y: cursor point
w,h: sensitivity/slop (in pixels)
push old setup first, so can pop it later
Week 4, Wed 24 Sep 03
© Tamara Munzner

31. Render Modes glRenderMode(mode) GL_RENDER: normal color buffer
default
GL_SELECT: selection mode for picking
(GL_FEEDBACK: report objects drawn)
Week 4, Wed 24 Sep 03
© Tamara Munzner

32. Name Stack “names” are just integers glInitNames() flat list
glLoadName(name)
or hierarchy supported by stack
glPushName(name), glPopName
can have multiple names per object
stack is at least 64 levels deep
Week 4, Wed 24 Sep 03
© Tamara Munzner

33. Hierarchical Names Example
for(int i = 0; i < 2; i++) { glPushName(i); for(int j = 0; j < 2; j++) { glPushMatrix(); glPushName(j); glTranslatef(i*10.0,0,j * 10.0); glPushName(HEAD); glCallList(snowManHeadDL); glLoadName(BODY); glCallList(snowManBodyDL); glPopName(); glPopName(); glPopMatrix(); } glPopName(); }
Week 4, Wed 24 Sep 03
© Tamara Munzner

34. Hit List glSelectBuffer(buffersize, *buffer)
where to store hit list data
on hit, copy entire contents of name stack to output buffer.
hit record
number of names on stack
minimum and minimum depth of object vertices
depth lies in the z-buffer range [0,1]
multiplied by 2^32 -1 then rounded to nearest int
Week 4, Wed 24 Sep 03
© Tamara Munzner

35. Separate Pick Function?
use same function to draw and pick
simpler to code
name stack commands ignored in render mode
customize functions for each
potentially more efficient
can avoid drawing unpickable objects
Week 4, Wed 24 Sep 03
© Tamara Munzner

36. Select/Hit advantages disadvantages faster flexible precision
OpenGL support means hardware accel
only do clipping work, no shading or rasterization
flexible precision
size of region controllable
flexible architecture
custom code possible, e.g. guaranteed frame rate
disadvantages
more complex
Week 4, Wed 24 Sep 03
© Tamara Munzner