Questions tagged [vector]

A mathematical concept that can be used to express position, direction or velocity and which can simplify or outright trivialise spatial problems.

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53
votes
4answers
55k views

What are normal, tangent and binormal vectors and how are they used?

I would like to find out the following information: What are they? Example usage in game development (the area they are used in) About the following vector types: ...
38
votes
5answers
21k views

In 2D, how do I efficiently find the nearest object to a point?

I have a sizable game engine and I'd like a feature for finding the nearest of a list of points. I could simply use the Pythagorean theorem to find each distance and choose the minimum one, but that ...
35
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2answers
5k views

Calculating the rotational force of a 2D sprite

I am wondering if someone has an elegant way of calculating the following scenario. I have an object of (n) number of squares, random shapes, but we will pretend they are all rectangles. We are ...
31
votes
3answers
67k views

How can I find the perpendicular to a 2D vector?

I'm making a top down game where the player moves forwards towards the position of the mouse cursor. As part of the player's movement code, I need to determine a vector that is perpendicular to the ...
28
votes
6answers
7k views

If a 3D vector represents a point, how can it have a length?

I am trying to understand vector arithmetic (and specifically its use in the Unity engine). I am not able to figure out how a vector can have a length (magnitude) even though it only represents a ...
27
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5answers
38k views

How can I calculate the angle and proper turn direction between two 2D vectors?

I am working on some movement AI where there are no obstacles and movement is restricted to the XY plane. I am calculating two vectors, v, the facing direction of ship 1, and w, the vector pointing ...
26
votes
3answers
9k views

How can I rotate an object based on another's offset to it?

I have a 3D model of a turret that con rotate around the Y-axis. This turret has a cannon that is significantly off the center of the object. I want the cannon, not the turret, to aim at a specified ...
21
votes
3answers
1k views

What's so different/complicated/useful about vectors?

Forgive me if this isn't considered a real question, but it is something I am genuinely confused about. I constantly hear other game developers talk about how using vectors are very useful, but also ...
21
votes
5answers
19k views

Do I need the 'w' component in my Vector class?

Assume you're writing matrix code that handles rotation, translation etc for 3d space. Now the transformation matrices have to be 4x4 to fit the translation component in. However, you don't actually ...
21
votes
1answer
8k views

Determine arc-length of a Catmull-Rom spline to move at a constant speed

I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1. ...
20
votes
6answers
15k views

Vectors in game development

I'm new to programming and game programming. I've reading something about vectors and math, but I have a question - where do I use vectors in game programming? Maybe anyone can give a simple example ...
18
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7answers
9k views

What's the best way of transforming a 2D vector into the closest 8-way compass direction?

If you have a 2D vector expressed as x and y, what's a good way of transforming that into the closest compass direction? e.g. ...
18
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7answers
2k views

Do I need a Point and a Vector object? Or just using a Vector object to represent a Point is ok?

Structuring the components of an engine that I am developing along with a friend (learning purposes), I came to this doubt. Initially we had a Point constructor, like the following: ...
17
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2answers
41k views

How do I use the dot product to get an angle between two vectors?

I am learning to use normalized vectors in my games. I've learned that in order to know the angle between two vectors, I can use the dot product. This gives me a value between -1 and 1, where 1 ...
17
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2answers
39k views

How do I linearly interpolate between two vectors?

I have a velocity vector where my client is at and where its going, and I have the same vector that comes from the server telling where the client should be. Sometimes its a bit different, so I want ...
15
votes
2answers
3k views

Shooting the bullet out of the gun instead of the camera, yet keeping it accurate with respect to the reticle

I'm working on a first person game, and I've ran into a problem. In my game, there's the player's gun being rendered, as well as a reticle in the center of the screen - like this: First, Let's ...
15
votes
1answer
3k views

How do I tell if my enemy can see my player?

Given a player and an enemy with position, and given the direction vector of each, how can I tell if one can "see" the other? In other words, how do I test if one position with direction is in front ...
14
votes
5answers
805 views

Can I simplify the inequality "distance(p1, p2) < distance(p1, p3)?"

I am working on some vector logic, so am asking: can I save processor time by simplifying this inequality: ...
14
votes
2answers
3k views

What are some good examples of the practical usages of cross product in game development?

I know how to calculate cross product, and know that the cross product of 2 vectors is a third vector that is perpendicular to a plane created by the first 2 vectors. However, I have not seen any good ...
14
votes
2answers
2k views

Dynamic thruster balancing of space ship

The space ships in my game a meant to be player-built with an arbitrary amount of thrusters attached anywhere with any rotation. I currently have some dirty code to rotate the ship to a given angle (...
11
votes
2answers
526 views

How do I find a point on a line?

I have two points (A, B) and the length of d. How can I find point C?
11
votes
2answers
12k views

In Unity, why is adding a Vector2 and a Vector3 ambiguous but assigning isn't?

Given the following two vectors: Vector3 v3 = Vector3.one; Vector2 v2 = Vector2.one; This line is ambiguous: ...
11
votes
2answers
6k views

How to calculate the vector of an interception?

Given are a twodimensional space, and 1 friendly spaceship standing still, one foe is moving NOT directly to the friendly ship with known actual position, speed and direction. The friendly ship wants ...
11
votes
1answer
3k views

Downprojecting an imaginary 4D mesh to the screen

As a mental exercise, I'm trying to imagine projecting an arbitrary 4D mesh onto the screen (2D). I'm guessing a single 4D triangle would still consist of only 3 points, however each of those 3 ...
10
votes
3answers
17k views

Get points on a line between two points

I'm making a simple space game in JavaScript, but now I've hit a wall regarding vectors. The game view is top-down on a 2d grid. When the user clicks on the grid, the space ship will fly to that ...
10
votes
3answers
11k views

How do I interpret the dot product of non-normalized vectors?

I know that if you take the dot-product of two normalized vectors, you get the cosine of the angle between them. But if I take the dot-product of two non-normalized vectors (or one normalized, one ...
10
votes
4answers
3k views

How does normal mapping really work?

I'm trying to grasp the concept of normal mapping, but I'm confused by a few things. In short, I'm not sure whether a normal map is viewpoint dependent or not (i.e. whether you'll get a different ...
10
votes
2answers
8k views

How do I determine if one polygon completely contains another?

I have 2 polygons. I know the vertex coordinates of both polygons. What's the best way to check if one is completely inside the other? For example, the algorithm should only recognize the black ...
9
votes
5answers
9k views

Why can't I use the operator '>=' with Vector3s?

I am trying to get a rectangle to move between two positions which I refer to as _positionA and _positionB. Both are of type <...
9
votes
1answer
4k views

How can I get the normal vector for a plane from a set of vertices?

I'm working on a HLSL / C++ little project to going over my graphics work, and I am unsure how I am to get a facing vector from a vertex polygon. I can't seem to find the formula. The positions are ...
9
votes
3answers
14k views

Is there a good cross-platform C++ vector graphics library out there? [closed]

I'm making a game and want to use vector graphics. I started re-coding it using Cairo and the performance is horrific. So, I'm looking for a different library. It needs to be for C++ and cross-...
9
votes
2answers
17k views

How do I find the angle between two vectors?

I have 3 points on my screen: ...
9
votes
1answer
3k views

Rotate object to face player

This is probably a simple vector question, but I'm not sure how to do it. I have an object at vector position (ox,oy). Potentially every update, the user walks ...
9
votes
2answers
20k views

Moving a sprite in XNA/C#, using vectors

I'm currently looking into XNA game development with the C# language. I have two classes: the main game handler and a "sprite" class. Following is some basic pseudo-code which I hope adequately ...
9
votes
2answers
10k views

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 ...
9
votes
4answers
1k 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 ...
9
votes
3answers
9k views

How do I calculate collision response between a sphere and a plane?

I'm trying to create a simple 3D game and need to constrain the player within the limits of the game world. When the player hits the sides of the world I want the player's ship to bounce off slightly. ...
8
votes
3answers
2k views

Vector3 vs. Vector2 - performance, usage?

I'm currently playing around with XNA, and creating a simple 2D platformer. I was thinking of adding multiple layers to make it a little bit of challenge. In stead of having a ...
8
votes
3answers
2k views

How can I check if a player-drawn line follows a path?

I want to draw an invisible path that the user must follow. I've stored that path as points. When a player draws a line, how can I test if it follows the path I've stored? Here's an example for ...
8
votes
2answers
7k views

How can I draw a line of certain length and direction?

I want to create a line of certain length and direction. What I mean by this is drawing a line from Point A to Point B. Normally in Unity C# to draw a line from Point A to Point B is simply: ...
8
votes
1answer
6k views

Unity: transform.LookAt(target) not "looking at" target?

I have been troubleshooting a prefab for several hours and am out of ideas. It concerns a method that I thought I was comfortable with, transform.LookAt(target). I have this prefab: As you can see, ...
8
votes
2answers
2k views

Rotate a vector

I want my first-person camera to smoothly change its viewing direction from direction d1 to direction d2. The latter direction is indicated by a target position t2. So far I have implemented a ...
8
votes
2answers
1k views

How do I find the closest points(thereby forming a polygon) enclosing a particular point?(see image)

I am working with a game engine, and my task is to add code for simulating fracture of rigid meshes. Right now I'm only working on breaking a cube. I am using Voronoi's algorithm to make a (...
8
votes
3answers
1k views

Collision detection problems using AABB's

I implemented a simple collision detection routine using AABB's between my main game sprite and various platforms (Please see code below). It works great, but I'm now introducing gravity to make my ...
8
votes
4answers
10k views

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 ...
8
votes
1answer
643 views

How do I prevent jitter amongst near-stationary physics objects?

I have been implementing a custom physics engine, and I'm pretty close to having it working as I would like it to. There is a gravitational force, collisions and collision response. Unfortunately, ...
7
votes
2answers
9k views

Line Intersection from parametric equation

I'm sure this question has been asked before. However, I'm trying to connect the dots by translating an equation on paper into an actual function. I thought It would be interesting to ask here instead ...
7
votes
1answer
26k views

What's the 'proper' way to get unit vectors?

My apologies if I've misunderstood the term 'unit vector' or misapplied it in concept, but I think that is the term for an object's heading when expressed as [x, y] ...
7
votes
3answers
8k views

Implementing Separating Axis Theorem (SAT) and Minimum Translation Vector (MTV)

I was following codezealot's tutorial on SAT and MTV and trying to implement it myself but I've come a cropper when it comes to getting the correct MTV. Here is my example: (Cue pretty pictures...) I'...
7
votes
2answers
3k views

Vector games (Wireframe, Elite-like) theory and implementations?

I'm interesting in knowing more about how vector games like Elite and Star Wars Atari were built from grounds up. The question is not how to implement vector graphics with modern 3D APIs like OpenGL ...

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