# Questions tagged [linear-algebra]

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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### 2D Collision detection: rewinding to moment of first intersection

I am working on a collision system in a Platformer tile-based game. All tiles are AABB. I am trying to implement "Rewind to Moment of First Intersection" mentioned in this post's second point. The ...
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### What is a good algorithm for generating a linear regression of positions in 3D space? (for getting the direction of a thrown object in VR)

I'm trying to get throwing to feel right in my VR game. I don't plan on actually using physics to do this; my idea is to accurately determine the lateral direction of the throw, then move the object ...
146 views

### How do I detect collisions between a point and a sloped line?

The character in my game constantly falls due to gravity, so i have to detect the collision between the bottom point of the character and the tile slope line on the same x coordinate. The character ...
51 views

### How to vary the initial velocity of a jump based on hold time?

What I want to do is, the longer player holds the screen, the longer distance the object will jump when they release the hold. Here is my code: ...
15 views

### Calculating the position of a third person camera from its right vector

I have a 3rd person camera, that always looks at the player from a certain distance. It updates its x and z position around the player in relation to the yaw value received from x axis mouse input. I ...
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### How to mirror a vector through some other vector?

I have a player's direction (playerDirection). I want to fire two bullets, one rotated by -30f, and one by 30f, so it looks like this: Blue line is the ...
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### Account for scale offset?

I have an odd situation where I know the position of an item on a mouse click and I know the panning state of a 2D camera pointing at it. So what I do is render an object at the point in which the ...
37 views

### Moving point (as line)-Polygon collision detection

i've reached a good point with my engine, with static/instant collision detection and callbacks in case of collision. By instant collision detection i mean: Object A moves from x1y1 to x2y2 Check if ...
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### How to create a custom set of coordinates based on two points in Unity?

As the title says, I am having problems finding a way to create a new set of local coordinates based on two points. Here is an example: Consider that the two gameObjects are not one parent of another,...
184 views

### How to detect least distance to line segments calculation

I'm trying to calculate the distance of the player to a few lines that intersect two points, and return the smallest distance (i.e. tell me which of the lines the player is closest to/how far the ...
101 views

### Finding translation component of a 4x4 matrix inverse

I have 4x4 matrix (A) (maya softw): ...
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### Applying multiple forces on a particle

If I have a particle, say in a polar coordinate grid, and I want to apply multiple vectors to it, how can I calculate where it's final position will be given those vectors? Ex. Imagine there's a ...
82 views

### Getting the Closet Points between Polygons with the GJK Algorithm

I am trying to implement the GJK algorithm by following this lecture. For the most part, it is working, but sometimes 1 of the 2 closest points is incorrect. Here are two examples: EXAMPLE 1: The ...
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### Leading a target with edge casting

I am trying to write a movement prediction code. I have found the quadratic method with these topics: : How to calculate shot angle and velocity to hit a moving target? : http://...
481 views

### Convert global 3d coordinate system to a local one with specific direction

Imagine a (x,y,z) coordinate system within a solar system, with (0,0,0) beeing the center of sun where Z axis goes thru both solar poles. I'm standing on a planet inside a house within that solar ...
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### 2D converting absolute top-down coordinates into relative third-person coordinates

I'm working on 2D top down zombie game. I started working on it as having a static 2D map and on every tick you update the coordinates of every object, including the player itself relative to the ...
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### How can I add acceleration to the movement of an object in a game

Below is the code that I'm using to move an object: ...
33 views

### How to get 60fps animation in terms of rounding/truncating position/alpha floats

I am wondering what gives the best animation performance running at 60fps with lots of objects. I have seen in a few places such as this that you should round or truncate your values so you don't get <...
69 views

### Define a circle from a point on its circumference and an angle

I'm working on a 2D, top-down driving game with some basic AI vehicles. The AI Vehicles move along a bidirected graph of positions. Each vehicle has a current position (from the graph) and a target ...
648 views

### Check whether a vector is to the left or right of another position

I don't know how to decide if my point is on the left or right side of another object. My first thought was to check if x-axis of object1 is bigger or smaller than object2's, but if my objects rotate ...
153 views

### How do I create the formula for calculate the damage of a skill

I'm trying to calculate the output damage of a skill. The skill can go up from level 1 to 100, it can scale with own levels and the attack of the character. Here some parameters Edit: I need a ...
392 views

### Find extreme points of a rotated ellipse function on a given axis

How to find the points where it is most extreme on the X and Y axis? For example lets say I have an equation that describes an ellipse that is rotated: ...
2k views

### Benefit of using Vector2 data type over separate x & y variables

I'm really curious about why a lot of people and game engines use Vector2 as its coordinate system instead of the traditional x and y value. Is there any benefit to this? I feel like it's just slow ...
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### Calculating the shadow cast by triangle onto the YZ plane

So, one of the exercises for my computer graphics class is as follows: Calculate the shadow cast by triangle T onto the YZ plane P. given: Triangle T coordinates: A=(30,10,16) B=(32,11,18) C=(31,...
245 views

### How to determine if an object is within field of view given xyz of object, player position, and 3D vector for player view?

I only have the object's position, the player position, and the vector representing the player's view, and I have the FoV (120 degrees horizontal/60 on each side, and 60 degrees vertical/30 on each ...
134 views

### detecting if a chess move is valid for a given pawn , preferably using Linear algebra

I'm making a chess game, where you simply drag and drop a pawn on the board with respect to each player's turn. when it comes to dropping a pawn we need to validate weather the move is allowed. for ...
2k views

### What does a linear transformation preserve?

They say an affine transformation preserves points, lines, parallel lines etc. I can see this if I think in terms of translation [Is there any other affine transformation you can give as an example, ...
119 views

### Trying to use 3D vectors for a 2D ping pong game

I am trying to setup a virtual ping pong table, and am getting a little stuck in trying to understand how to do 3D vector math and render it in 2D. So far, my plan is for the ball: X = up/down, Y = ...
63 views

### Calculate smooth transition between local space angles

I'm trying to calculate direction of moving character (to rotate it's animation). I have something like this: Character can have 4 cardinal directions. The rotation is calculated from the current ...
1k views

### OpenGL calculate circle rotation around a given point

I'm trying to rotate an object around a certain point. If this point is the center of my world space I use the following algorithm: glm::vec3 center is the center ...
113 views

### How to Calculate Caridnal Direction from Unit Vector

I have unit Vector of acceleration in local space of object. Now I want to calculate Cardinal Direction from (North, East, South, West). So Far I tried to: ...
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### How do I calculate a point between two points with a given distance percentage? [duplicate]

I've made a simple drawing: The distance between these two points is calculated with a simple formula: Which gives: 5,38 I need to calculate the green point's coordinates, which is set at 80% ...
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### What is FRotationMatrix in Unreal engine 4?

I am working on FPS shooter example in Unreal engine 4 documentation. One of the lines for forward movement of pawn is ...
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### Turret aiming code

I'm currently working on turret aiming code. If I can't hit the center of the object (due to an obstacle), I want to see if I can hit any of the object. To do this i'll get it's bounds, and check in ...
568 views

### 2d Scale width and height based on distance

I'm drawing a health bar on top of each player. I transform 3d position to 2d. I would like to draw it smaller when distance increases. Any simple math for that? Let's say bar width is 30 and height ...
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### How to mirror/reflect/flip a 4D transformation matrix

I am importing my animation keyframe joint data from Blender to my game engine. The joint data is a set of 4D matrices. Things are looking good except a remaining issue where the animation is facing ...
187 views

### How to calculate a normalized direction of two rotations?

In Vector math and translations we can do: dir = (v1 - v2).norm and then v1.translate(dir * 50) so ...
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### How to determine if the player between two points?

I'm making a skating game and I'm having trouble figuring out how to snap the player onto grinds and rails in between multiple points. My plan was to snap the player onto a point in between the two ...
80 views

### Intersection point of two lines with given formula

I have following formula to check the intersection of two line segments: ...
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### interace between C and Lua function with 3D vector arguments [closed]

I have C++ function (which runs some physical simulation inside my game engine) which looks like this: ...
1k views

### Calculating the distance from a line to a point in 2D

I have a simple setup: How do I calculate the orange distance? It's the distance between the block on the left to the white line in the center (X & Z axes combined). I don't have the ...
730 views

### How can I make players move diagonally at equal speeds?

In a tile-based 2D RPG, a character is supposed to walk into all eight directions. However, if we blindly tell the player to move in the direction (1, 1), he will be around 41% (√2-fold) faster. Thus,...
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### Determine if the player should be able to interact with a door

You know the drill, standard first person door mechanics. How do they do it? My most noticeable and frustrating problem is when there is a door within range and in view, but the closest door is ...
268 views

### Why Change from one coordinate system to another?

When dealing with affine transformations, why do we need to change from one frame to another? What are some reasons. What are the pros and cons of doing this and the limitations if this was not ...
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### Scaling a sphere to give identical result, regardless of rotation

how can I maintain a consistent scaling of a sphere regardless of the rotation of the model? For example, take the following (scaled) sphere: In this image, we start with a sphere, looking at it ...
3k views

### Need help with getting a direction vector between two given points

I need to find the angle of rotation from a bullet traveling from point A to point B, like in my attached diagram. I tried searching, but I got a little lost in which exact formula to use. I want to ...
284 views

### Problem calculating screen point for a point in a 3D world with view matrix and projection matrix

I am trying to calculate the 2D screen point of a 3D world position. For this I use the multiplication ViewMatrix * ProjectionMatrix. But I am not getting good ...