plane

I have many points inside a square. I want to partition the square in many small rectangles and check how many points fall in each rectangle, i.e. I want to compute the joint probability distribution of the points. I am reporting a couple of common sense approaches, using loops and not very efficient: % Data N = 1e5; % number of points xy = rand(N, 2); % coordinates of points xy(randi(2*N, 100, 1)) = 0; % add some points on one side xy(randi(2*N, 100, 1)) = 1; % add some points on the other side xy(randi(N, 100, 1), :) = 0; % add some points on one corner xy(randi(N, 100, 1), :) = 1; % add

Dear fellow stackoverflow users, I am trying to calculate the normal vectors over an arbitrary (but smooth) surface defined by a set of 3D points. For this, I am using a plane fitting algorithm that finds the local least square plane based on the 10 nearest neighbors of the point at which I'm calculating the normal vector. However, it does not always find what seems to be the best plane. Thus, I'm wondering whether there is a flaw in my implementation or a flaw in my algorithm. I'm using Singular Value Decomposition as I found recommended in several links on the subject of plane fitting. Here

I've been able to apply a smooth animation to my sprite and control it using the accelerometer. My sprite is fixed to move left and right along the x-aixs. From here, I need to figure out how to create a vertical infinite wavy line for the sprite to attempt to trace. the aim of my game is for the user to control the sprite's left/right movement with the accelerometer in an attempt to trace the never ending wavy line as best they can, whilst the sprite and camera both move in a vertical direction to simulate "moving along the line." It would be ideal if the line was randomly generated. I've

I have a 3d point, defined by [x0, y0, z0] . This point belongs to a plane, defined by [a, b, c, d] . normal = [a, b, c] , and ax + by + cz + d = 0 How can convert or map the 3d point to a pair of (u,v) coordinates ? This must be something really simple, but I can't figure it out. First of all, you need to compute your u and v vectors. u and v shall be orthogonal to the normal of your plane, and orthogonal to each other. There is no unique way to define them, but a convenient and fast way may be something like this: n = [a, b, c] u = normalize([b, -a, 0]) // Assuming that a != 0 and b != 0,

I have a plane defined by a normal (n) and a distance (d) (from the origin). I would like to transform it into a new system. The long way is like this: 1) multiply distance (d) with normal (n) resulting in a a vector (p) 2) rotate (R) and translate (v) the vector (p) to get (p') 3) normalize (p') to get the normal 4) use another algorithm to find the smallest distance (d') between the new plane and the origin I haven't tried this but I guess it should work. QUestion: Isn't there a faster way to get n' and d'? If the translation (v) is 0 than I can skip 4). But if it is not 0? Is there an

In 3D space I am trying to determine if a ray/line intersects a square and if so, the x and y position on the square that it intersects. I have a ray represented by two points: R1 = (Rx1, Ry1, Rz1) and R2 = (Rx2, Ry2, Rz2) And the square is represented by four vertices: S1 = (Sx1, Sy1, Sz1), S2 = (Sx2, Sy2, Sz2), S3 = (Sx3, Sy3, Sz3) and S4 = (Sx4, Sy4, Sz4). I’ve found lots of algebraic equations for this online but none seem to fit this problem exactly. Ideally I would like the answer in Java code, but an equation that I can easily convert to code will do also. All help will be appreciated.