你的世界中的每個邊界都是一條線。該線的一側是固體，另一側不是。你試圖計算的正常值是該線的等式的一部分。它指向該行的非固體一側。直線方程的另一部分是從直線到原點的距離。該線的方程可以從該線上的兩個點找到。您可以根據遊戲空間中您想要牆的座標來定義這兩點。
法線通過旋轉由兩個點90度定義的線段然後標準化來計算。
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;
}
您正在使用的首選後臺緩衝區的寬度和高度來定義你的世界空間，讓你會用這些來定義用於計算法線點。
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));
請注意，點必須以順時針順序給出，以使正常點的方向正確。
下XNA 4.0程序演示了使用這些概念：
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);
}
}
}
這是一個很好的解決方案，有沒有雖然做的更優雅的方式？我覺得在製作這款遊戲時我會不斷地黑客入侵！ – JuniorDeveloper1208
不知道它是否更乾淨，但你可以爲枚舉創建一個擴展方法（例如'GetNormal（this CollideType collideType）'），它有一個開關，並返回每個標準的正常值... – Cameron
謝謝！我覺得代碼很簡單，但數學很難。網上沒有太多的文檔，反正也不是4.0。 – JuniorDeveloper1208