1. Terrain Sampled height-field 2D or 3D Shading Segmentation Smoothing
Iso-contours
Project 2: Color ground and lakes

2. 2D or 3D visualization?
Regular (x,y) grid, a scalar value (Z[x,y]) per sample
View as an image: map Z to color
View as height-field (map Z to height, and color)
Discuss Pros & Cons of each

3. Shading Color (hue…) depends on scalar value (height)
Non-linear mapping that helps interpretation
Intensity of reflected light depends on surface normal
Typically computed from a triangulation of the quad

4. Shading quads
Z[x,y]
(x,y)
(x+1,y)

5. Segmentation Split terrain into distinct regions.
How are regions defined? computed? visualized?
Examples of regions
Height spans
Normalize to total height range
Divide into spans (Number? Uniform?)
Assign color to each (snowy tops, green valleys)
Vary intensity or color ramp within each interval
By slope
Use different color for steep parts (grey cliffs)
By curvature
Concave, convex, saddle
Expected benefits of segmentation?
Possible drawbacks of segmentation?

6. Slope How to compute slope? C Map slope-to-color? B A Z[x,y] (x,y)
Split each quad into 2 or 4 triangles
Compute slope for each triangle
Map each slope to a color
Map slope-to-color? C B A
Z[x,y]
(x,y)

7. Curvature Classify each sample How? How to shade the surface? Concave
Convex
Neither
How?
How to shade the surface?

8. Smoothing Predict each height value C” from its neighbors.
Use average of cubic predictions in x and in y
Compute vector L2 towards predicted value
Move each height towards its predicted value
Repeat
How to identify outliers?
Acquisition errors
How to correct them?

9. Smoothing code
vec cubic (pt A, pt B, pt C, pt D, pt E) {return(new vec(
(-A.x+4*B.x-6*C.x+4*D.x-E.x)/6,
(-A.y+4*B.y-6*C.y+4*D.y-E.y)/6,
(-A.z+4*B.z-6*C.z+4*D.z-E.z)/6 ));}
vec cubicFitX(int i, int j) {
return(cubic(G[i-2][j], G[i-1][j],G[i][j],G[i+1][j],G[i+2][j] ));}
vec cubicFitY(int i, int j) {
return(cubic(G[i][j-2], G[i][j-1],G[i][j],G[i][j+1],G[i] [j+2] ));}
void XYcubicFilter() {
for(int k=0; k<20; k++) {
for (int i=2; i<n-2; i++) for (int j=2; j<n-2; j++) L[i][j]=average(cubicFitX(i,j),cubicFitY(i,j));
for (int i=2; i<n-2; i++) for (int j=2; j<n-2; j++) G[i][j].addScaledVec(0.5,L[i][j]);
}; }

10. Subdivision Double the resolution:
Subdivide in x (as discussed in earlier lecture)
Subdivide in y
Repeat if desired

11. Iso-contours Ch = All points of a given height h (green curves)
Closed loops (unless clipped by border of domain)
Iso-contours may be nested

12. Vertices of an iso-contour Ch
A vertex is height if its height > h, and low otherwise
An edge joining high & low vertices is a stick
How to estimate the point where Ch crosses the stick?
What assumption are we making?
z=h A B d 1
z=h A B d 1

13. Loops of an iso-contour Ch
Loop over all edges
If you find an unmarked stick trace its loop
marking all sticks that the loop crosses
How to trace a loop?
What if the loop hits the border?
pad domain with a very low border

14. How to order loops?
How to test whether whether a point is inside a loop?
How to test whether a loop is inside a loop?

15. Smoothing iso-contours loops
Deform iso-contour in 2D without crossing any grid sample
Constrain vertex to stay on its stick

16. Spill-over points, lake boundaries
What is a lake?
How to identify spill-over points?
How to define, represent, compute the surfaces of the lakes?

17. A lake may have islands How to identify island borders?
How to render such a lake?

18. Project 2: Ground color and lakes
Start with the terrain viewer code provided
Compute color-coding that distinguishes low (green), high (white), intermediate (brown), steep (grey).
Assign suitable color ramps to each based on height and argue why they are good.
Draw some 20 iso-contours using width 3 red curves
Identify all lakes and render their surface (flat) in semi-transparent blue color
Deliver:
Viewer: applet, instructions, source code
Report: 2 pages with images and references
Explain, justify, evaluate your solution for the color ramps and for the lake boundaries

19. Different visualizations

20. Questions Pros & const of 3D vs 2D terrain visualization
Pros & cons of segmentation
How to perform smoothing on a terrain data
How to identify and correct outliers
How to compute the vertices of an iso-contour
How to trace the loops of an iso-contour
How to identify saddle points and spill-over points