By Robert Bridson
A sensible advent, the second one variation of Fluid Simulation for special effects shows you the way to animate absolutely three-d incompressible move. It covers the entire points of fluid simulation, from the maths and algorithms to implementation, whereas making revisions and updates to mirror alterations within the box because the first edition.
Highlights of the second one Edition
The publication adjustments the order of issues as they seemed within the first variation to make extra feel while analyzing the 1st time via. It additionally comprises numerous updates by way of distilling writer Robert Bridson’s event within the visible results to focus on an important issues in fluid simulation. It promises an realizing of ways the elements of fluid simulation paintings in addition to the instruments for growing your personal animations.
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Additional info for Fluid Simulation for Computer Graphics, Second Edition
Without any bias, the natural formula is the first central difference: ∂q ∂x i ≈ qi+1 − qi−1 . 12) which is biased to the right and only accurate to O(∆x). 11) has a major problem in that the derivative estimate at grid point i completely ignores the value qi sampled there! To see why this is so terrible, recall that a constant function can be defined as one whose first derivative is zero. 11) is zero, we are allowing q’s that aren’t necessarily constant—qi could be quite different from qi−1 and qi+1 and still the central difference will report that the derivative is zero as long as qi−1 = qi+1 .
46 4. Level Set Geometry If we combine this with the fact that the value of φ is the distance (or negative distance inside) to the closest point, we get another useful fact: for any point x, x − φ(x)∇φ(x) is the closest point to x on the surface. Signed distance functions easily give us answers to the first two queries listed at the start of this chapter! Another beautiful consequence is that ∇φ(x) is the unit-length outwardpointing normal to the surface at the closest point to x on the surface.
3 Time Step Size A primary concern for any numerical method is whether it is stable: will it (or any of the numerical errors we make) blow up? Happily the semiLagrangian approach above is unconditionally stable: no matter how big ∆t is, we never blow up. It’s easy to see why: wherever the particle starting point ends up, we interpolate from old values of q to get the new values for q. Linear/bilinear/trilinear interpolation always produces values that lie between the values we’re interpolating from: we can’t create larger or smaller values of q than were already present in the previous time step.