Mathematics plays a fundamental role in video game development. I strongly recommend to study the basics of linear algebra to have a better control of what you create. However, in XNA there is a lot of support for analytical geometry. There are some complex algorithms already implemented so it’s extremely important to know what it is available.
You can manage positions, speeds and directions using the classes: Point, Vector2, Vector3 and Vector4.
Vector3 a = new Vector3(0, 0, 10);
a.Normalize();
float x = a.X;
float y = a.Y;
float z = a.Z;
float length = a.Length();
Vector3 b = Vector3.Right;
Vector3 c = a + b;
float distance = Vector3.Distance(a, b);
float dotProduct = Vector3.Dot(a, b);
Vector3 crossProduct = Vector3.Cross(a, b);
Vector3 trasform = Vector3.Transform(a, Matrix.CreateScale(5));
The most important class in XNA is the Matrix class:
Matrix identity = Matrix.Identity;
Vector3 cameraPosition = new Vector3(0, 0, 10);
Vector3 cameraTarget = Vector3.Zero;
Vector3 cameraUp = Vector3.Forward;
var viewMatrix = Matrix.CreateLookAt(cameraPosition, cameraTarget, cameraUp);
Matrix projectionMatrix = Matrix.CreatePerspectiveFieldOfView(
MathHelper.PiOver4,
GraphicsDevice.Viewport.Width / GraphicsDevice.Viewport.Height,
1, 100);
Matrix viewProjectionMatrix = viewMatrix * projectionMatrix;
var scale = Matrix.CreateScale(5);
var translation = Matrix.CreateTranslation(10, 20, 30);
var rotationX = Matrix.CreateRotationX(MathHelper.PiOver4);
var rotationY = Matrix.CreateRotationY(MathHelper.PiOver4);
var rotationZ = Matrix.CreateRotationZ(MathHelper.PiOver4);
var rotation = Matrix.CreateFromAxisAngle(new Vector3(1, 2, 3), MathHelper.PiOver4);
The Ray class represent a straight line. The Plane class represent a plane in the 3d world. Then there other important classes like Rectangle, BoundingBox, BoundingFrustum and BoundingSphere.
Rectangle rectangle1 = new Rectangle(0, 0, 10, 10);
Rectangle rectangle2 = new Rectangle(5, 5, 10, 10);
bool intersect = rectangle1.Intersects(rectangle2);
bool contains = rectangle1.Contains(new Point(10, 20));
Ray ray = new Ray(Vector3.Zero, Vector3.Forward);
Plane plane = new Plane(Vector3.Up, 10);
BoundingSphere sphere = new BoundingSphere(Vector3.One, 5);
BoundingBox box = new BoundingBox(Vector3.Zero, Vector3.One);
float? distance = ray.Intersects(plane);
PlaneIntersectionType pit = plane.Intersects(sphere);
ContainmentType ct = box.Contains(sphere);
BoundingFrustum frustum = new BoundingFrustum(ViewMatrix * ProjectionMatrix);
Vector3[] corners = frustum.GetCorners();
Plane nearPlane = frustum.Near;
Plane farPlane = frustum.Far;
With the class Curve is then possible to handle curves.
Finally, it is important to remember the class MathHelper that contains some useful methods
float max = MathHelper.Max(5, 10);
float min = MathHelper.Min(5, 10);
float piOver2 = MathHelper.PiOver2;
float degrees = MathHelper.ToDegrees(piOver2);
float radians = MathHelper.ToRadians(90);