10/23/2001 CS 638, Fall 2001

Today

• Terrain– Terrain LOD

10/23/2001 CS 638, Fall 2001

Terrain LOD

• As you have heard by now, terrain poses problems for static LOD methods– Must have high resolution in the near field, and low

resolution in the distance, all in one model

• Dynamic LOD methods are the answer– All based on the idea of cuts through a tree of potential

simplifications

• We will discuss the ROAM algorithm in detail– Other algorithms are similar in style, but this is the best

10/23/2001 CS 638, Fall 2001

Terrain is Easier!

• Assumption: We are starting with a height field defined on a regular grid– Assume it’s a square to make it easier

– We can mesh it by forming triangles with the data points

• The data is highly structured– Every data point has the same number of neighbors

– Every triangle can be the same size

– Hence, the tree of possible simplifications is very regular

• Still, multiple possibilities exist for the triangulation and the simplification operations

10/23/2001 CS 638, Fall 2001

Triangle Bintrees

• Binary trees in which:– Each node represents a right-angled isosceles triangle

– Each node has two children formed by splitting from the right angle vertex to the midpoint of the baseline

– The leaf nodes use vertices from the original height field

• Another way to build a spatial partitioning tree, but particularly well suited to simplification algorithms– Easy to maintain neighbor information

– Easy to avoid T-vertices

10/23/2001 CS 638, Fall 2001

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Triangle Bintree Example

10/23/2001 CS 638, Fall 2001

Bintree Data Structure

• Parent and child pointers

• Neighbors– A left neighbor, a right neighbor, and a base neighbor– Note that the base and right angle give us a way to orient the triangle– Neighbors are not necessarily at your own level

• Later, error bounds that say how much variation in height there is in your children

10/23/2001 CS 638, Fall 2001

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Cuts

10/23/2001 CS 638, Fall 2001

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Neighbors

• 5: left neighbor 6, right neighbor 9• 6: left neighbor 8, right neighbor 5• 7: left neighbor 8, base neighbor 10• 8: base neighbor 6, right neighbor 7• 9: base neighbor 5, left neighbor 10• 10: base neighbor 7, right neighbor 9

• Note that 8 is 6’s left neighbor but 6 is 8’s base neighbor– If you are someone’s left/right/base neighbor they are not always

your right/left/base neighbor

• In other words, neighbors need not come from the same level in the tree

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10/23/2001 CS 638, Fall 2001

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Not All Cuts Are Created Equal

Note the T-vertex - causes cracks in rendering

10/23/2001 CS 638, Fall 2001

Generating Cuts

• Cuts are generated by a sequence of split or merge steps– Split: Drop the cut below to include your children– Merge: Lift the cut up above two children

• To avoid T-vertices, some splits lead to other, forced, splits

• An LOD algorithm chooses which steps to apply to generate a particular triangle count or error rate

10/23/2001 CS 638, Fall 2001

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A Split

• A split cuts a triangle in two by splitting its base edge– If the base edge is on a boundary, just split, as shown

– If the base edge is shared, additional splits are forced

• Add a new triangle to the mesh

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10/23/2001 CS 638, Fall 2001

Forced Splits

• Triangles are always split along their base

• Hence, must also be able to split the base neighbor – Requires neighbors to be

mutual base neighbors

– If they are not base neighbors, even more splits are needed

– Simple recursive formulation

10/23/2001 CS 638, Fall 2001

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Merges

• A diamond is a merge candidate if the children of it’s members are in the triangulation– The children of the 7-10 diamond below are candidates– Look for parents of sibling leaf nodes that are base neighbors or

have no base neighbors

• Reduces the triangle count21

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10/23/2001 CS 638, Fall 2001

Refinement LOD Algorithm

• Start with the base mesh• Repeatedly split triangles until done

– Stop when a specific triangle count is reached, or …– Stop when error is below some amount

• To guide the split order, assign priorities to each split and always do the one with the highest priority– After each split, update priorities of affected triangles– Sample priority: High priority to splits that will reduce big errors

• What is the complexity of this? (Roughly)• A similar algorithm works by simplifying the mesh through

merge operations. Why choose one over the other?

10/23/2001 CS 638, Fall 2001

Refinement Notes

• If the priorities are monotonic, then the resulting terrain is optimal– Monotonic: Priorities of children are not larger than that of their

parent

• Priorities can come from many sources:– In or out of view, silhouette, projected error, under a vehicle, line of

sight, …

• Does not exploit coherence: As the view moves over the terrain, the triangulation isn’t likely to change much

• We should be able to start with the existing triangulation, and modify it to produce the new optimal triangulation

10/23/2001 CS 638, Fall 2001

Dual Queue Optimization

• Have the split queue, as before• Have a merge queue:

– Queue of potential merges, with priority as the max of the split priority for the triangles in each merge

• Repeat until target size/accuracy and the max split priority is less than the min merge priority– If the mesh is too large/accurate, do the optimal merge

• Update data structures appropriately

– Otherwise, do the optimal split• Update data structures appropriately

10/23/2001 CS 638, Fall 2001

Why Does it Work?

• The merge queue priorities tell you how much error you would add by doing each merge

• The split queue tells you how much error you would remove by doing each split

• A merge frees up two triangles, while a split takes at least one• If you can free some triangles with a merge and use them with a

more effective split, then you win– The min in the merge queue is the least error you can add with a merge– The max in the split queue is the most error you can remove with a split– If you can trade a split for a merge and save some error, then do it

10/23/2001 CS 638, Fall 2001

Projected Error Metrics

• Idea is to figure out how far a sequence of merges moves the terrain from its original correct location– Measured in screen space, which is what the viewer sees

• Start with bounds in world space, and then project the bounds at run-time– World space bounds are view independent

– Projected screen space bounds are view dependent

10/23/2001 CS 638, Fall 2001

World Space Bounds

• With terrain, merge only moves points up or down• Bound how far a point can move with a wedgie

– A bintree triangle extruded up and down to contain its children– Defined by d, the thickness of the extrusion

• Fast to compute, so works for dynamic terrain– Important for explosion craters and the like

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10/23/2001 CS 638, Fall 2001

Performance Bottlenecks

• Storing and managing priorities for out-of-view triangles is a waste of time– Do standard frustum culling to identify them

• Sending individual triangles is wasteful– Build strips as triangles are split and merged

• Naively, at every frame, wedgies must be projected, new priorities computed and the queues re-sorted– Use the viewer’s velocity to bound the number of frames before a

priority could possibly make it to the top of a heap– Delay recomputation until then

• Priority queue: Bin priorities to reduce sorting cost– At low priorities, order within bins doesn’t matter

10/23/2001 CS 638, Fall 2001

Additional Enhancements

• Stop processing after a certain amount of time– Easily done: just stop processing the next split or merge

– Result no longer optimal, but probably not bad

• Cost of dual queue algorithm depends on the number of steps required to change one mesh into another– Check ahead of time how many steps might be required

– If too may, just rebuild mesh from scratch using refinement algorithm

• Can get accurate line-of-sight or under-vehicle height by manipulating priorities to force certain splits

10/23/2001 CS 638, Fall 2001

Other Algorithms

• Algorithm from Lindstrom et al is essentially the same idea as the ROAM refinement algorithm– Based on square blocks of (triangulated) terrain

• Makes determining forced splits harder

– Slightly different error bounds

• An algorithm from the game community:– For a particular split operation, the viewer distance is the primary

error factor– For each split, store distance at which it should occur– Check current mesh on each frame for splits/merges according to

viewer distance– Non-optimal, but gets rid of priority queues (the big cost)

10/23/2001 CS 638, Fall 2001

Midterm Info

• Thursday in class• Bring in:

– Something to write with

– A ruler (it will be helpful)

– A double sided letter sized sheet with anything on it (except things that increase the surface area)

10/23/2001 CS 638, Fall 2001

Project Next Stage

• LithTech does almost everything we have talked about in the last six weeks

• So, the next stage is going to be done mostly in OpenGL (or similar)– Light maps

– Stencil-buffer shadow volume algorithms

• LOD in LithTech