Blobby Modelling Alex Benton

What is it? z“Metaball, or ‘Blobby’, Modelling is a technique which uses implicit surfaces to produce models which seem more ‘organic’ or ‘blobby’ than conventional models built from flat planes and rigid angles”. --me

Examples-- Paul Bourke (1997)

Examples-- “New Train” - Wyvill

Examples-- “Cabrit Model” - Wyvill

Uses of Blobby Modelling zOrganic forms and nonlinear shapes zScientific modelling (electron orbitals, some medical imaging) zMuscles and joints with skin zRapid prototyping zCAD/CAM solid geometry

How does it work? zEach point in space generates a field of force, which drops off as a function of distance from the point. zA blobby model is formed from the shells of these force fields, the implicit surface which they define in space.

How does it work? (Bourke 1997) zSeveral force functions work well. Examples: y“Blobby Molecules” - Jim Blinn xF(r) = a e -br 2 xHere ‘b’ is related to the standard deviation of the curve, and ‘a’ to the height.

How does it work? (Bourke 1997) zSeveral force functions work well. Examples: y“Metaballs” - Blinn again (I think) xF(r) = { a(1- 3r 2 / b 2 )0 <= r < b/3 { (3a/2)(1-r/b) 2 b/3 <= r < b { 0b <= r xHere ‘a’ is a scaling factor and ‘b’ bounds the radius of effect.

How does it work? (Bourke 1997) zSeveral force functions work well. Examples: y“Soft Objects” - Wyvill & Wyvill xF(r) = a(1 - 4r 6 /9b r 4 /9b r 2 / 9b 2 ) xThis function is basically the first few terms in the series expansion of an exponential function. x‘a’ scales the function, and ‘b’ determines radius of influence. xAdvantage : rapid computation.

How does it work? (Bourke 1997) zForce functions comparison:

How does it REALLY work? zOnce you have your force function, the next task is to actually find the implicit surface. zYou already know one technique for this : Marching Cubes. zHowever, marching cubes is very accurate and detailed; working at lower levels of precision is difficult.

How does it REALLY work? zIntroducing : OCTREES. zAn Octree is a recursive subdivision of space which “homes in” on the surface, from larger to finer detail, and then uses similar techniques to Marching Cubes approximate the implicit surface with polygons. zOctrees can display initial approximations of the surface immediately.

How does it REALLY work? zBecause the octree is a cube in space, you evaluate the force function F(r) at each vertex of the cube. zThis allows you to polygonalize the cube, in the same manner as Marching Cubes. zTo refine the polygonalization, you subdivide the cube into eight subcubes, discarding any child whose vertices are all hot or all cold.

How does it REALLY work? zRecursive subdivision:

How does it REALLY work? zRecursive subdivision:

How does it REALLY work? zRecursive subdivision:

How does it REALLY work? zFind the edges, separating hot from cold:

How does it REALLY work? zFor each Octree with hot and cold corners, you can find the best-fitting polygons that approximate that surface. The edges of the polygons pass through points linearly interpolated along the edges of the cube. yT = (0.5 - F(P1)) / (F(P2) - F(P1)) yP = P1 + T * (P2 - P1)

Pros and Cons zBenefits: yVery rapid general shapes yAllows rapid manipulation at multiple levels of detail ySurface complexity is not a function of data complexity yEnables a “poor man’s” solid geometry

Pros and Cons zDownsides: yFlat surfaces, sharp angles, etc. are difficult yDifficult to precisely achieve targetted features y“popping” between levels can be misleading

What else? zComplex primitives! yWhy settle for a point when you could have a line? Or a spline? zColors and textures yThe same math that blends forces can blend textures and colors as well. zMany other avenues of research currently open...

YAMM (Yet Another Metaball Modeller) zYAMM is my hobby and research work. zIt’s not polished software. It’s home made. zAvailable from J:\Staff Folders\Alex Benton\YAMM

Sources for more info... zhttp://astronomy.swin.edu.au/~pbourke/modelling/implicitsurf/ zhttp://pages.cpsc.ucalgary.ca/~blob/ zhttp:// - Octrees zD. Ricci A Constructive Geometry for Computer Graphics Computer Journal, May 1973 zJules Bloomenthal Polygonization of Implicit Surfaces Computer Aided Geometric Design, Issue 5, 1988 zBrian Wyvill, Craig McPheeters, Geoff Wyvill Animating Soft Objects The Visual Computer, Issue zBrian Wyvill, Craig McPheeters, Geoff Wyvill Soft Objects Advanced Computer Graphics (Proc. CG Tokyo 1986)