你的世界中的每一个边界都是一条线。线的一侧是实心的，另一侧不是。您尝试计算的法线是该线等式的一部分。它指向线的非实心侧。直线方程的另一部分是直线到原点的距离。可以从该线上的两个点找到该线的方程。您可以根据游戏空间中想要墙壁的坐标来定义这两个点。
法线是通过将两点定义的线段旋转 90 度然后归一化来计算的。
public static Vector2 ComputeNormal(Vector2 point1, Vector2 point2)
{
Vector2 normal = new Vector2();
normal.X = point2.Y - point1.Y;
normal.Y = point1.X - point2.X;
normal.Normalize();
return normal;
}
您正在使用首选的后台缓冲区宽度和高度来定义您的世界空间，因此您将使用它们来定义用于计算法线的点。
float left = 0.0f;
float right = graphics.PreferredBackBufferWidth;
float top = 0.0f;
float bottom = graphics.PreferredBackBufferHeight;
Vector2 topNormal = ComputeNormal(new Vector2(left, top), new Vector2(right, top));
Vector2 bottomNormal = ComputeNormal(new Vector2(right, bottom), new Vector2(left, bottom));
请注意，点必须按顺时针顺序给出，以便法线指向正确的方向。
以下 XNA 4.0 程序演示了这些概念的使用：
using System;
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Graphics;
using Microsoft.Xna.Framework.Input;
namespace WindowsGame
{
public class Ball
{
const int DIAMETER = 40;
const float RADIUS = DIAMETER * 0.5f;
const float MASS = 0.25f;
const int PIXELS = DIAMETER * DIAMETER;
static readonly uint WHITE = Color.White.PackedValue;
static readonly uint BLACK = new Color(0, 0, 0, 0).PackedValue;
Texture2D m_texture;
Vector2 m_position;
Vector2 m_velocity;
public Ball(GraphicsDevice graphicsDevice)
{
m_texture = new Texture2D(graphicsDevice, DIAMETER, DIAMETER);
uint[] data = new uint[PIXELS];
for (int i = 0; i < DIAMETER; i++)
{
float iPosition = i - RADIUS;
for (int j = 0; j < DIAMETER; j++)
{
data[i * DIAMETER + j] = new Vector2(iPosition, j - RADIUS).Length() <= RADIUS ? WHITE : BLACK;
}
}
m_texture.SetData<uint>(data);
}
public float Radius
{
get
{
return RADIUS;
}
}
public Vector2 Position
{
get
{
return m_position;
}
}
public Vector2 Velocity
{
get
{
return m_velocity;
}
set
{
m_velocity = value;
}
}
public void ApplyImpulse(Vector2 impulse)
{
Vector2 acceleration = impulse / MASS;
m_velocity += acceleration;
}
public void Update(float dt)
{
m_position += m_velocity; // Euler integration - innaccurate and unstable but it will do for this simulation
}
public void Draw(SpriteBatch spriteBatch)
{
spriteBatch.Draw(m_texture, DrawRectangle, Color.White);
}
private Rectangle DrawRectangle
{
get
{
int x = (int)Math.Round(m_position.X - RADIUS);
int y = (int)Math.Round(m_position.Y - RADIUS);
return new Rectangle(x, y, DIAMETER, DIAMETER);
}
}
}
public class Boundary
{
private Vector2 m_point1;
private Vector2 m_point2;
private Vector2 m_normal;
private float m_distance;
public Boundary(Vector2 point1, Vector2 point2)
{
m_point1 = point1;
m_point2 = point2;
m_normal = new Vector2();
m_normal.X = point2.Y - point1.Y;
m_normal.Y = point1.X - point2.X;
m_distance = point2.X * point1.Y - point1.X * point2.Y;
float invLength = 1.0f / m_normal.Length();
m_normal *= invLength;
m_distance *= invLength;
}
public Vector2 Normal
{
get
{
return m_normal;
}
}
public void PerformCollision(Ball ball)
{
float distanceToBallCenter = DistanceToPoint(ball.Position);
if (distanceToBallCenter <= ball.Radius)
{
ResolveCollision(ball);
}
}
public void ResolveCollision(Ball ball)
{
ball.Velocity = Vector2.Reflect(ball.Velocity, m_normal);
}
private float DistanceToPoint(Vector2 point)
{
return
m_normal.X * point.X +
m_normal.Y * point.Y +
m_distance;
}
}
public class World
{
Boundary m_left;
Boundary m_right;
Boundary m_top;
Boundary m_bottom;
public World(float left, float right, float top, float bottom)
{
m_top = new Boundary(new Vector2(right, top), new Vector2(left, top));
m_right = new Boundary(new Vector2(right, bottom), new Vector2(right, top));
m_bottom = new Boundary(new Vector2(left, bottom), new Vector2(right, bottom));
m_left = new Boundary(new Vector2(left, top), new Vector2(left, bottom));
}
public void PerformCollision(Ball ball)
{
m_top.PerformCollision(ball);
m_right.PerformCollision(ball);
m_bottom.PerformCollision(ball);
m_left.PerformCollision(ball);
}
}
public class Game1 : Microsoft.Xna.Framework.Game
{
GraphicsDeviceManager graphics;
SpriteBatch spriteBatch;
Matrix viewMatrix;
Matrix inverseViewMatrix;
Ball ball;
World world;
public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = "Content";
IsMouseVisible = true;
}
protected override void Initialize()
{
spriteBatch = new SpriteBatch(GraphicsDevice);
ball = new Ball(GraphicsDevice);
float right = Window.ClientBounds.Width * 0.5f;
float left = -right;
float bottom = Window.ClientBounds.Height * 0.5f;
float top = -bottom;
world = new World(left, right, top, bottom);
viewMatrix = Matrix.CreateTranslation(Window.ClientBounds.Width * 0.5f, Window.ClientBounds.Height * 0.5f, 0.0f);
inverseViewMatrix = Matrix.Invert(viewMatrix);
base.Initialize();
}
private void ProcessUserInput()
{
MouseState mouseState = Mouse.GetState();
Vector2 mousePositionClient = new Vector2((float)mouseState.X, (float)mouseState.Y);
Vector2 mousePositionWorld = Vector2.Transform(mousePositionClient, inverseViewMatrix);
if (mousePositionWorld != ball.Position)
{
Vector2 impulse = mousePositionWorld - ball.Position;
impulse *= 1.0f / impulse.LengthSquared();
ball.ApplyImpulse(-impulse);
}
}
protected override void Update(GameTime gameTime)
{
if (GamePad.GetState(PlayerIndex.One).Buttons.Back == ButtonState.Pressed)
this.Exit();
float dt = (float)gameTime.ElapsedGameTime.TotalSeconds;
ProcessUserInput();
ball.Update(dt);
world.PerformCollision(ball);
base.Update(gameTime);
}
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.Clear(Color.CornflowerBlue);
spriteBatch.Begin(SpriteSortMode.Deferred, null, null, null, null, null, viewMatrix);
ball.Draw(spriteBatch);
spriteBatch.End();
base.Draw(gameTime);
}
}
}