How can we use vector and scalar in games? What benefit from that.
Could someone please indicate precisely the difference between a scalar and a vector in games field ? I find no matter how many times I try to understand but I maybe need examples for that.
A scalar is just another word for a number. The distinction is that a scalar is a number that is part of a vector. There is nothing special about a scalar.
A vector is a set of numbers (one or more) that define something, in the most common case you have 2 numbers representing a 2D vector or 3 numbers representing a 3D vector. The abstract notion for a vector is simply an arrow.
Take a piece of graph paper. Select any point on that paper and call it the origin. Its coordinate will be x = 0, y = 0. Now draw a straight line from that point in any direction and any length. To describe that arrow you need to define the vector. Count how far across the page the end of the arrow is from the start (origin) and that is the x component. Then how far up the page and that is the y component.
You have just created a vector that has two numbers (x,y) that completely describe the arrow on the paper. This type of vector always starts at zero. You can also describe the vector by its direction (ie north, east, south...) and length.
In 3D you need 3 numbers to describe any arrow. (x,y,z)
Vectors are very handy. You can use a vector to describe how fast something is moving and in what direction. The vector represents a little arrow that starts where the object is now and ends where the object will be in the next time unit.
Thus an object at coordinate x,y has a vector velocity(0.2,0.3). To calculate the position of the object in the next time unit just add the vector to the coordinate
newXPos = currentXPos + velocityVectorX
newYPos = currentYPos + velocityVectorY
If you want to slow the speed by half you can multiply the vector by 0.5
velocityVectorX = velocityVectorX * 0.5
velocityVectorY = velocityVectorY * 0.5
You do the same to increase the speed.
velocityVectorX = velocityVectorX * 2
velocityVectorY = velocityVectorY * 2
You may have an object in 3D space that has many forces acting on it. There is gravity a vector (arrow) pointing down (G). The force of the air resistance pointing up (R). The current velocity another arrow pointing in the direction it is traveling (V). You can have as many as you like (need) to describe all the forces that push and pull at the object. When you need to calculate the position of the object for the next instance in time (say one second) you just add all the force vectors together to get the total force as a vector and add that to the objects position
Object.x = Object.x + G.x + R.x + V.x;
Object.y = Object.y + G.y + R.y + V.y;
Object.z = Object.z + G.y + R.z + V.z;
If you just want the velocity
V.x = V.x + G.x + R.x;
V.y = V.y + G.y + R.y;
V.z = V.z + G.y + R.z;
That is the new velocity in one second.
There are many things that can be done with a vector. A vector can be used to point away from a surface in 3D, this vector is called a surface normal. The you create a vector from a point on that surface pointing to a light. The cosine of the angle between the two vectors is how much light the surface will reflect.
You can use a vector to represent the three direction in space an object has. Say a box, there is a 3D vector pointing along the width, another along the height and the last along the depth. The length of each vector represents the length of each side. You can make another vector to represent how far the corner of the box is from the origin (any known point) In 3D these 4 vectors are used to represent the object and is called a transformation matrix (just another type of vector made up of vectors)
The list of things vectors can do is endless.
The basics is just like number, you can add, subtract, multiply and divide and vector. Then there are a host of special functions for vectors, normalize, transform, dot product and cross product to name but a few. For these things people normally use a library that does all this for you. My view is that if you really want to learn about vectors and how they are used write your own vector library at some point until then use a library.
Hope that cleared the mud a little bit for you, it is always difficult to describe something you have used for a long time to someone that is new to it so feel free to ask questions in the comments if you need.