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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 …

Say the object is 10 meters above ground. Assume that our dt (delta t) is 1 second. The object goes to the height of 9 meters at the end of the first iteration Here lies your problem. It is true …

Your question is not precise enough. An array of points is only « clockwise » or « anti-clockwise » relative to a reference point. Otherwise, any array of three points can always be either CW or CCW. …

You need a unit vector tangent to the planet surface: v = normalize((pY - oY, oX - pX)) Then just multiply v by your force amount.

You do not need to do anything special: Perlin noise is a gradient noise and is designed to give you an interpolated value at any point, not just at the square corners. Just use your Perlin noise gene …

The direction vector of the red line is (CosTable[a], SinTable[a]). It is a unit vector. Now consider the green line on your drawing. The vector along this line pointing towards (x, y) is orthogonal …

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: …

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 …

The “velocity in a space” can be broken down in two vectors, one that is the same direction as a, and one that is perpendicular to a. The first vector has direction u and size su, computed as follows …

First of all, for uniformly distributed data, Knuth’s function i * 2654435761 >> 16 is definitely better than i * 2654435761 >> 8 because it shuffles more bits. An explanation follows. Consider the m …

If vector (x,y) is a tangent vector of your curve, then the normal vector is simply (y,-x). So you just need to find a tangent vector, and it all depends on how exactly you define the curve. If your …

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) …

Here’s a little example. Suppose you slerp q0 and q1 with a value of t = 0.2 and a value of t = 0.4. This gives you a quaternion s(0.2) and a quaternion s(0.4). Quaternion multiplication also gives us …

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 …

It’s not always the best method, and it can be more computationally expensive (though this ultimately depends on how you store your data), but I will make the argument that lerping 2D values works rea …