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Long ago I developed an multiprocessor raytracing renderer for an old supecomputer in my college. I addressed this problem by defining an observation point and the screen plane in world coordinate. T …

What about Bézier curve? A segment is basically a first degree BC but you can construct second or superior degrees curves that are still segments. I suggest to you to use a cubic BC having the two con …

Let's complicate your spiral: be in your case f(t) := t, in mine f(t) := 1 (so i pay back my complications with simplifications :) If you want to go at a certain speed in this degenerate spiral (a …

Talking about percentage, you can generate an integer number from 0 to 99 than subdivide your 100% into chunks of different sizes: | 10 | 10 | 20 | 30 | 30 | 1 5 2 …

The fourth dimension in 3D vector is used to compute the affine transformations that will be impossible to compute using matrixes alone. The space remains three-dimensional so this mean that the fourt …

The path finder should give you the path and you should not modify that. I belive that it is possible to modify your path finder algorithm to take into account that path with sharp turns are wrose tha …

The library should not be a problem for your project. If it is your case that means that you are coupling your system with a library: this generally is not good idea. What if another better library em …

Let A and B be your vectors: The summing vectors do not need to be unit vectors but simply equal in length so, if |A| >= |B|, you can: which is more numerically stable since you have only a frac …

Tring to answer to the appropriate comment of Natan, I did some consideration that can be useful to understand what really happens when you use vectors in Affine Space to represent 3D vectors in the s …

I'd rather cast shadow rays instead of line of sight rays. Let's say this is your view area (the potentially visible area) ###################### #####.............#### ###................### ##.... …

That vector can be obtained simply by summing up the normals of the boxes faces and normalize. The normal vector even point outside the box so the sum vector points toward the direction where the boxe …

If you can vary your speed (thus your angle of steer) you will always find a solution, starting from the degenerate one where the entity is almost stopped rotating in a little circle until pointing th …

The segment running from A to B can be computed as P(t) = A + D · t where D is B - A and t runs from 0 to 1 Now the circle is centered on the origin (move A and B if necessary to put the center in …

I'm assuming yours is a toroidal system, you can partition to the space so each unit has its sub area. At each step the particles are moved, the particles that goes out the sub area are sent to the r …