Extend static rendering mode to handle all grade objects in CGA mode about ganja.js HOT 8 OPEN

I'll look at adding instanced rendering for static objects (where available) - it should speed things up substantially on modern architectures. I'll also add an option to decide on the tesselation of the circles and spheres as totals do run up quickly there. (spheres are 8192 triangles now, so 500 of them makes 4 million .. )

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Sounds fantastic, thanks Steven!

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Hi Hugo, Steven,

@hugohadfield
As you noted you were rending large numbers of planes, would you mind sharing an example of your rendering?

I met a problem in rending sheet elements in CGA. I want them centered at diffrent points.
In my ten-line code toy example, it seems that the sheets/planes are centered along x-axis, not at the specified points.

@enkimute
Is it an rendering issue?
Maybe I shouldn’t represent them as CGA planes?

Thank you very much in advance,
Hongying

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Hi Hongying, planes in the conformal model are inherently infinite, therefore it is pretty arbitrary to define a positional point to draw them in 3d... if you want specific spatial localisation it would probably be better to represent them via triangular facets which ganja also supports!

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Thank you, Hugo.
I thought in rendering an infinite plane, the location of the center is a rendering preference of ganja.
So we could not specify the location of a bivector either?

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I'm afraid it isn't a rendering option, perhaps if you dig into the source code you may be able to add one but it would be seperate to the multivector representation of the planes themselves... When you mention bivectors what specific bivectors do you mean? Point pairs are renderable, and due to being a "round" are inherently localisable, I'm not sure if ganja support flat points and some of the other bivector interpretations

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I forgot to mention a space in saying "bivector". I mean bivector in general (still this is too vague :( ).

For example, according to "Geometric Algebra for Computer Science", we can obtain "the tangent to a flat or to a round passing through one of its points p" by p \rfloor \hat{X} (p is a point on X, p ^ X = 0) (on page 445, Eq 15.1, Figure 15.6). So I assume specifying a bivector at certain point is not an algebraic problem, and is a rendering issue.

Similarly, there is a figure illustrating different type of vectors (free, normal, line, and tangent vector) on page 452.

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Hi ying17zi,

The parametrisation ganja.js uses is different from the one GA-viewer has, and focuses mostly on the representations dictated by the outer product null space (to display element A, show the collection of all points x for which x^A=0). (and you can use it side-by-side to the implicit visualizer). Because of this mindset, it renders for example point-pairs as a pair of points and not as a line (although there is an option for that : {useUnnaturalLineDisplayForPointPairs:true}. For planes, the automatic display is centered, but it is quite easy to render two triangles instead, given four points a,b,c,d , simply do this.graph([[a,b,c],[a,c,d]],{gl:true, conformal:true}).

A rewrite of the renderer is coming up (which will allow mixing of implicit and parametrised representations), I'll make sure to see how much more of the GAViewer functionality I can include (I will also discuss this with Dr Dorst).

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