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In general, there is no parabola that goes through three given points. However, if you loosen the problem constraints and only define the Y coordinate of the parabola’s top and allow its X coordinate …

On a 40×40 square of pixels, you can draw a circle with approximately 40×sqrt(8) pixels. If you are looking for a circle drawing algorithm to let you pick the pixels to put in your array, an easy way …

Reasonable approximation As already stated in other answers, there is no exact way to do this. However, it is possible to efficiently approximate a solution. My formula will only handle the upper ri …

You do not need the angle itself, just the direction, which is given by vector End - Start. For convenience it's good to normalise that vector, ie. divide it by its length. You will then extrapolate o …

All you need is atan2: angle = atan2(frontwheel.y - rearwheel.y, frontwheel.x - rearwheel.x);

When used together with exp, the log function is commonly understood as the natural logarithm. You are actually using base 10 logarithm (which would be log10 in C++). Fortunately you can get the same …

The derivative of the ball position is: dx/dt = vx dy/dt = vy + gravity * t So the derivative of the parabola arc length s is, using Pythagora’s theorem: ds/dt = sqrt(vx² + (vy + gravity * t)²) …

Since the algorithm already parses all edges of the polygon to see how many times a ray cast from test crosses them, I think it's reasonable to add a check to see whether test lies on the edge exactly …

Your game is a nontransitive game. You can implement it with 3 stats R, P and S, using the rock-paper-scissors logic. Call these stats whatever you want, but I'll stick with the RPS logic. Now suppos …

Despite its name, Vector3.Transform() does not transform a vector but a point. The unwanted side effect is that the translation part gets added to your vector. If you want to actually transform a vect …

I need a way of translating a set of points P I suppose you mean rotating here? Let Z = (0,0,1). If cross(N,Z) has length 0, it means that all your points already lie in the desired plane. Other …

Beware of the argument order here. Here is what atan2 will give you: atan2(x,z) is the angle between the (x,0,z) vector and the +Z axis in the Z-X plane. atan2(z,x) is the angle between the (x,0,z) …

The distance between the centre of the circle (x1,y1) and the target (x2,y2) is: D = sqrt((x1-x2)² + (y1-y2)²) So the distance between the target and any point on the circle varies between D - r an …

Here is a more numerically stable (for large values) way of getting Log(Fn) where Fn is the nth Fibonacci number. Let φ = (1 + sqrt(5)) / 2 and ψ = (1 - sqrt(5)) / 2. Then the nth Fibonacci number is: …

Let b be the angle between vectors p1p2 and p1p3. Its value can be computed as: b = pi - atan2(p1p3.y, p1p3.x) The angle between p1p4 and p1p3 is b-a. Since p1p3p4 is a right-angled triangle, we kn …