Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. The tag is generally used for questions regarding calculations over vectors.

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21
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Are there 3D projections other than orthographic and perspective? [closed]

The question is pretty much in the title. Are there notable 3D projections other than orthographic and perspective that could be used in a 3D system such as OpenGL? In particular, are there any that ...
20
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6answers
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What is a good linear algebra book for game programmers? [closed]

I was told that I should start learning Linear Algebra in order to create good games with good physics. I'm reading Linear Algebra book and it's completely foreign to me. The author starts out with ...
12
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3answers
977 views

Biased, conservative random walk

I have a sprite which has Velocity and Position, either stored as Vector2. At each Update cycle, velocity is added to the position. I would like to give the sprite a third vector, Target. New targets ...
9
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2answers
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How can I test if a point lies between two parallel lines?

In the game I'm designing there is a blast that shoots out from an origin point towards the direction of the mouse. The width of this blast is always going to be the same. Along the bottom of the ...
9
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4answers
209 views

How do I correctly project a point behind the camera?

I am making a 3D game in which I put an exclamation marker above points of interest. In order to find out where in the 2D screen should I put my marker, I am manually projecting the 3D point where ...
8
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3answers
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How can I reverse the effect of a transformation matrix?

I have recently been working on a game with using OpenGL and C++ through GLFW. In the game I have an airship with a turret mounted on it. The airship moves around in world space coordinates and the ...
8
votes
4answers
920 views

Moving objects colliding when using unalligned collision avoidance (steering)

I'm having trouble with unaligned collision avoidance for what I think is a rare case. I have set two objects to move towards each other but with a slight offset, so one of the objects is moving ...
7
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2answers
9k views

How to detect 2D line on line collision?

I'm a flash actionscript game developer who is a bit backward with mathematics, though I find physics both interesting and cool. For reference this is a similar game to the one I'm making: Untangled ...
7
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2answers
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How can you extract orientation from a transformation matrix?

I have a 4x4 transformation matrix M, and I want to find out the shape of a sphere when transformed by M. (Sphere is at the origin and has radius 1.) I know I can find the center by just multiplying ...
7
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4answers
4k views

How do I find the intersection of two lines

I have a bounding box on my character, its position in the previous frame an the current frame. The bounding box is axis aligned. My character is running around inside a cave, I have a list of ...
7
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2answers
272 views

Draw land for motocross game

I would like to draw a land for a motocross game. I've been thinking of Bezier Curves but I am not sure whether this is the best approach. Can you give me some advice? I want to do it in JavaScript, ...
7
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3answers
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Rotating a vector by another vector in shader

I have a terrain surface with a normal for each point on the terrain. I have a second detail normal map to be applied to the terrain. These normals are in 3-space. The Y value of both normals is ...
7
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0answers
189 views

What is Direction Cosines applications in game development? [closed]

I am reading about direction of cosines which it seems to tie into change of axial system(transform of one coordinate system to another) and its just not clicking in my head. I don't know if its the ...
6
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1answer
245 views

Matrices: Arrays or separate member variables?

I'm teaching myself 3D maths and in the process building my own rudimentary engine (of sorts). I was wondering what would be the best way to structure my matrix class. There are a few options: ...
6
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1answer
2k views

Ray Intersecting Plane Formula in C++/DirectX

I'm developing a picking system that will use rays that intersect volumes and I'm having trouble with ray intersection versus a plane. I was able to figure out spheres fairly easily, but planes are ...
5
votes
3answers
1k views

For normal mapping, why can we not simply add the tangent normal to the surface normal?

I am looking at implementing bump mapping (which in all implementations I have seen is really normal mapping), and so far all I have read says that to do this, we create a matrix to convert from ...
5
votes
1answer
162 views

Vector Math question

Suppose I have two game object located at two Vector3s v1 and v2, respectively. If I wanted to locate a position between v1 ad v2, but 3 units away from v2, how would I manage that in terms of ...
5
votes
1answer
519 views

How can I calculate a vertex normal for a hard edge?

Here is a picture of a lovely polygon: Circled is a vertex, and numbered are its adjacent faces. I have calculated the normals of those faces as such (not yet normalized, 0-indexed): Vertex 1 ...
5
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1answer
697 views

Rotating plane to be parallel to given normal via change of basis

I have two planes and their respective normals. I would like to rotate the second plane, planeB, so that it is parallel to the first, planeA. To do this, I am using a change of basis to rotate each ...
4
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3answers
2k views

Tetris - Rotations using Linear Algebra (Rotation Matrices)

I'm making Tetris in Java and am at the point of rotations... Originally I was hardcoding each rotation: if (direction.equals("right")) { if (shape.equals("Bar")) { if ...
4
votes
2answers
7k views

View matrix in opengl

Sorry for my clumsy question. But I don't know where I am wrong at creating view matrix. I have the following code: createMatrix(vec4f(xAxis.x, xAxis.y, xAxis.z, dot(xAxis,eye)), vec4f( ...
4
votes
3answers
807 views

What is a direction vector and why should it be normalized?

I've been trying to get the hang of vectors and I read Wolfire's blog about linear algebra and I seem to understand most stuff except when it comes to storing a direction as a vector and using it by ...
4
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4answers
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What is an efficient 2D line-segment-versus-triangle intersection test?

In a 2D plane, I have a line segment (P0 and P1) and a triangle, defined by three points (t0, t1 and t2). My goal is to test, as efficiently as possible ( in terms of computational time), whether the ...
4
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1answer
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Raycasting tutorial / vector math question

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 ...
4
votes
1answer
327 views

Line plane intersection: what is this variable?

I'm doing line plane intersection, and have come across an un-referenced variable or constant in the tutorial I'm following. One of the formulae given is this: t = N dot (p2 – p0) ...
4
votes
2answers
521 views

Enemy mathematical behavior

I'm really trying to up my game in game mathematics and now I'm working on enemy movement and a bit of AI. I have an enemy with two modes attack and avoid, based on an integer avoid variable that's ...
4
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1answer
2k views

Points on lines where the two lines are the closest together

I'm trying to find the points on two lines where the two lines are the closest. I've implemented the following method (Points and Vectors are as you'd expect, and a Line consists of a Point on the ...
3
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3answers
2k views

Equation to make small number big and big number small (gravity)

I have a sprite that I want to speed up as it gets closer to another object. I really want this to flow well and don't want a series of if statements. All I can think of is to take the distance and ...
3
votes
2answers
721 views

How to find point on a circle that's opposite another point?

How do I find the coordinate of point and angle value on circle sprite which placed on opposite side of sprite from a touch point and the center point of the sprite? I know A position, B position and ...
3
votes
4answers
4k views

Line triangle intersection - last bits

I'm doing line-triangle intersection. I have found the intersection point (vector) on the plane. All I need to do now is work out whether the point is inside the triangle it collided with (not the ...
3
votes
1answer
1k views

Gerstner wave function simplified?

The gerstner wave function is a commonly used method to calculate waves and simulate water in video games and movies or most 3d simulations. It is however quite complex so it is very hard for young ...
3
votes
1answer
170 views

How to calculate where specular highlights converge with an anisotropic shader?

If you look at a rendering with an anisotropic shader applied you will notice that there are special spots on the 3D surface/mesh where the lights seems to converge, a point where a given vector ...
3
votes
1answer
52 views

Finding coordinate in radius

Hello i have two points (Vector3) A and B. And have a radius r How can i find a coords of point P in a circle by angle?
3
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1answer
450 views

Mixing Perspective and Orthographic Projections?

I'm going to start with some background, so jump to my question at the bottom for the TLDR version. Problem: In a Japanese 4gamer article (english translation via Chev on Polycount) explaining some ...
3
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3answers
260 views

Portal View/Projection Matrix near plane

For RenderToTexture/Camera based portal rendering, the basics seems simple enough. However, with a free camera, most of the time it is going to be looking at such portals at an angle: Now a ...
3
votes
1answer
176 views

Make an object slide around an obstacle

I have path areas set up in a game I'm making for canvas/html5 and have got it working to keep the player within these areas. I have a function isOut(boundary, x, y) that returns true if the point is ...
2
votes
2answers
227 views

Angle between two planes

I have two triangles in 3d space which share 1 edge and I would like to determine if the angle between their normal vectors is "uphill" or "downhill". In other words, if you set one flat, would the ...
2
votes
1answer
559 views

3d Water Simulation formula questions

I have created a Grid: At each point along the grid, is a vertex (Intersection Points): Each of these points has an x,y,z position. Vector3f(x,y,z). In an attempt to animate the grid into a group ...
2
votes
2answers
346 views

Java Tetris - Matrix Rotations

I'm building Tetris in Java and am trying to use linear algebra to rotate a piece composed of 4 tiles. My friend was explaining the way to do it is: He said: "To clarify, you do need to rotate ...
2
votes
2answers
435 views

2D field of view detection inverted

I'm not sure if the title matches what I'm actually facing I'm trying to test if I can see a point is in my field of view (in the context of an NPC seeing in it's direction.) I know that: cos0 = ...
2
votes
2answers
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Dot Product Vs Cross Product Turning a Turret Towards A Enemy and firing

http://pastebin.com/iw9DHf7s is code demonstrating dot product turning a turretto a target and firing. It works and chooses best angle to spin. A problem can occur when game goes faster (better ...
2
votes
1answer
152 views

Getting half plane direction relative from cam position

Im implementing certain Camera movements in my turn based games. I'm able to place and rotate the camera between two units that attack each other. However it will always move to the same "side". Which ...
2
votes
1answer
14k views

Transform between two 3d cartesian coordinate systems

I'd like to know how to get the rotation matrix for the transformation from one cartesian coordinate system (X,Y,Z) to another one (X',Y',Z'). Both systems are defined with three orthogonal vectors as ...
2
votes
1answer
319 views

How to correctly represent a bone system?

I'm currently representing my bone system as follows, in pseudocode: root = {} root.rot = v3(0,0,0) root.pos = v3(0,0,0) function create_child(parent,rot,length): child_bone = {} ...
2
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1answer
226 views

Optimising skeletal animation

I am implementing a skeleton system for my latest game. I am using my own linear algebra classes which already have some optimisations, such as separate transformPoint and transformVector functions ...
2
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0answers
34 views

Arma 3 - How to calculate height of a thought line over a known spot in 3rd person view?

Assuming a player object with third-person-view is in a 3d room and the center of the screen has a dot - let's call it "cursorTarget". All I have is the position of the player, the position 5 meters ...
2
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0answers
129 views

Typical Applications of Linear System Solver in Game Developemnt [closed]

I am going to write a custom solver for linear system. I would like to survey the typical problems involved the linear system solving in games. So that I can custom optimization on these problems ...
2
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1answer
448 views

How to linearly transform vertices for large coordinate systems

Alright, so I'm working on a space game and well, I want it to have a lot of space! So I need a large coordinate system and for my rendering pipeline to not suffer from "vertex jittering" due to ...
1
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2answers
858 views

Matrix Rotation with three Angles

I want to rotate a form with three given angles fo each of the three axis. But the GLM rotation function takes only one angle and a vector as arguments. How can I convert between both formats?
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2answers
375 views

Learning C++, algorithms and vectorial algebra [closed]

I need your recommendations for a good study source about videogame orientated C++, algorithms and vectorial algebra. I will be applying to a videogame programmer course in January so I need to start ...