Raycasting tutorial / vector math question

Posted by mattboy on Game Development See other posts from Game Development or by mattboy
Published on 2012-12-05T19:03:20Z Indexed on 2012/12/05 23:21 UTC
Read the original article Hit count: 475

Filed under:

vector

|

ray-casting

|

raycasting

|

vector-algebra

I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question.

In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel from 1 x-side to the next x-side, or from 1 y-side to the next y-side, in the square grid that makes up the world map (see below screenshot).

enter image description here

In the tutorial they are calculated as follows, but without much explanation:

//length of ray from one x or y-side to next x or y-side
double deltaDistX = sqrt(1 + (rayDirY * rayDirY) / (rayDirX * rayDirX));
double deltaDistY = sqrt(1 + (rayDirX * rayDirX) / (rayDirY * rayDirY));

rayDirY and rayDirX are the direction of a ray that has been cast.

How do you get these formulas? It looks like pythagorean theorem is part of it, but somehow there's division involved here. Can anyone clue me in as to what mathematical knowledge I'm missing here, or "prove" the formula by showing how it's derived?

© Game Development or respective owner

Related posts about vector

vector iterator not dereferencable at runtime on a vector<vector<vector<A*>*>*>

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi, I have this destructor that create error at runtime "vector iterator not dereferencable". The gridMatrix is a std::vector<std::vector<std::vector<AtomsCell< Atom<T> * > * > * > * > I added the typename and also the typedef but I still have the error. I will move… >>> More
Adding Functions to an Implementation of Vector

as seen on Stack Overflow - Search for 'Stack Overflow'
I have this implementation of vector that I've been working on for a few days using examples from a textbook: #include <iostream> #include <string> #include <cassert> #include <algorithm> #include <cstring> // Vector.h using namespace std; template <class T> class… >>> More
Making only the outer vector in vector<vector<int>> fixed

as seen on Stack Overflow - Search for 'Stack Overflow'
I want to create a vector<vector<int>> where the outer vector is fixed (always containing the same vectors), but the inner vectors can be changed. For example: int n = 2; //decided at runtime assert(n>0); vector<vector<int>> outer(n); //outer vector contains n empty vectors outer… >>> More
(R) How can I get the complement of vector y in vector x

as seen on Stack Overflow - Search for 'Stack Overflow'
That's x \ y using mathematical notation. Suppose x <- c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,1,1,3) y <- c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1) How can I get a vector with ALL the values in x that are not in y. i.e the result should be: 2,1,1,3 There is a similar question here… >>> More
C++: Appending a vector to a vector

as seen on Stack Overflow - Search for 'Stack Overflow'
Assuming I have 2 STL vectors: vector<int> a; vector<int> b; Let's also say the both have around 30 elements. How do I add the vector b to the end of vector a? The dirty way would be iterating through b and adding each element via push_back, though I wouldn't like to do that! >>> More

Related posts about ray-casting

3D Ray Casting / Picking

as seen on Game Development - Search for 'Game Development'
Hi, I am not sure if I should post this link, but I feel this falls into game development just as much as it does math. I have a ray cast's far and near values and I am trying to calculate the end point of the ray so that I can either draw a line to show the ray, or render an object at the end of… >>> More
3D collision detection with meshes using only raycasting?

as seen on Game Development - Search for 'Game Development'
I'm building a game using WebGL and Three.js, and so far I have a terrain with a guy walking on it. I simply cast a ray downwards to know the terrain height. How can I do this for other 3D objects, like the inside of a house? Is this possible by casting many rays in every direction of the player… >>> More
Writing the correct value in the depth buffer when using ray-casting

as seen on Game Development - Search for 'Game Development'
I am doing a ray-casting in a 3d texture until I hit a correct value. I am doing the ray-casting in a cube and the cube corners are already in world coordinates so I don't have to multiply the vertices with the modelviewmatrix to get the correct position. Vertex shader world_coordinate_ = gl_Vertex; Fragment… >>> More
Raycasting tutorial / vector math question

as seen on Game Development - Search for 'Game Development'
I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question. In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel… >>> More
How can I draw an arrow at the edge of the screen pointing to an object that is off screen?

as seen on Game Development - Search for 'Game Development'
I am wishing to do what is described in this topic: http://www.allegro.cc/forums/print-thread/283220 I have attempted a variety of the methods mentioned here. First I tried to use the method described by Carrus85: Just take the ratio of the two triangle hypontenuses (doesn't matter which triagle… >>> More