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# Truly curved surfaces

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Is there a way to make mathamatically curved surfaces? The equations to make different types of 3 dimensional curved surfaces arn''t THAT complicated. A REAL (simulated) curved surface using 0 polygons would be fun to have.

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Sure there is. Since it''s relatively trivial to calculate the normal to a curve (just take the negative reciprocal of the derivative of the curve at each sampled point), you just need to take a sample of the shapes for each pixel. Essentially, we''re talking about ray tracing or similar method.

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merlin, have you seen this been done? .sen

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merlin mentioned some of this, but you seem to not understand.

look into nurbs. most of them tesselate pretty much any amount of polys you want, including up to the point where you cpu/video card chokes and you want a very long time for the image.

polygons are simply a method of reducing the work, well, technically the tessilation process simplifies how things can be thought of when break up the curve you are drawing.

for truly non-polygonal curved surfaces. look into ray tracers like pov-ray. they actually attempt to simulate light whne rendering objects via mathmatically equations and boolean operations of some built in objects (like spheres, cylinders, etc). no polygons at all (though you can import meshes to be rendered with your scene). just realize that cpus are not fast enough currently to make realtime ractracing at an acceptable quality the average gamer is used to (you have to run at low resolution, interpolate, and use other hacks to increase speed but also reduce quality).

the reality is there is no point in having a simulated curve that uses 0 polys, since nothing accelrates that currently. also using no polys does not make a curved surface real. some of the video cards (radeon, geforce3) even accelerate some curved surfaces (ones that use bezier patches) and look pretty good as well.

try a search on google for ray tracers though.

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