Ily*_*lya 2 xna linear-algebra
编辑:只是想提出我更清楚的问题.我几乎无法看到像Matrix.CreateTransformationZ这样的东西不仅在矩阵乘法的情况下工作,更重要的是它对屏幕空间/世界空间的作用,所以我可以得到更清晰的图像.因此,也许有人可以改变代码或给我一个简短的片段来测试我可以使用它来围绕轴旋转和/或绕轴旋转.我也改变了这个例子.
因此,我仍然难以直观地了解矩阵如何与xna屏幕空间一起工作.
我给你举个例子:
public class Game1 : Microsoft.Xna.Framework.Game
{
Texture2D shipTexture, rockTexture;
Vector2 shipPosition = new Vector2(100.0f, 100.0f);
Vector2 rockPosition = new Vector2(100.0f, 29.0f);
int count;
float shipRotation, rockRotation;
float rockSpeed, rockRotationSpeed;
bool move = true;
const int rock = 0;
const int ship = 1;
Color[] rockColor;
Color[] shipColor;
float testRot = 0.0f;
Vector2 shipCenter; int shipWidth, shipHeight;
Vector2 rockCenter; int rockWidth, rockHeight;
GraphicsDeviceManager graphics;
SpriteBatch spriteBatch;
#region maincontent
public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = "Content";
}
/// <summary>
/// Allows the game to perform any initialization it needs to before starting to run.
/// This is where it can query for any required services and load any non-graphic
/// related content. Calling base.Initialize will enumerate through any components
/// and initialize them as well.
/// </summary>
protected override void Initialize()
{
// TODO: Add your initialization logic here
rockSpeed = 0.16f;
rockRotationSpeed = 0.3f;
base.Initialize();
}
/// <summary>
/// LoadContent will be called once per game and is the place to load
/// all of your content.
/// </summary>
protected override void LoadContent()
{
shipTexture = Content.Load<Texture2D>("Images\\ship");
rockTexture = Content.Load<Texture2D>("Images\\asteroid");
rockWidth = rockTexture.Width; rockHeight = rockTexture.Height;
shipWidth = shipTexture.Width; shipHeight = shipTexture.Height;
rockCenter = new Vector2(rockWidth / 2, rockHeight / 2);
shipCenter = new Vector2(shipWidth / 2, shipHeight / 2);
// Create a new SpriteBatch, which can be used to draw textures.
spriteBatch = new SpriteBatch(GraphicsDevice);
// TODO: use this.Content to load your game content here
rockColor = new Color[rockTexture.Width * rockTexture.Height];
rockTexture.GetData(rockColor);
shipColor = new Color[shipTexture.Width * shipTexture.Height];
shipTexture.GetData(shipColor);
}
/// <summary>
/// UnloadContent will be called once per game and is the place to unload
/// all content.
/// </summary>
protected override void UnloadContent()
{
// TODO: Unload any non ContentManager content here
}
/// <summary>
/// This is called when the game should draw itself.
/// </summary>
/// <param name="gameTime">Provides a snapshot of timing values.</param>
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.Clear(Color.CornflowerBlue);
spriteBatch.Begin(SpriteBlendMode.AlphaBlend);
spriteBatch.Draw(rockTexture, rockPosition,
null, Color.White, testRot, rockCenter, 1.0f,
SpriteEffects.None, 0.0f);
spriteBatch.Draw(shipTexture, shipPosition,
null, Color.White, shipRotation, shipCenter,
1.0f, SpriteEffects.None, 0.0f);
spriteBatch.End();
// TODO: Add your drawing code here
base.Draw(gameTime);
}
#endregion
/// <summary>
/// Allows the game to run logic such as updating the world,
/// checking for collisions, gathering input, and playing audio.
/// </summary>
/// <param name="gameTime">Provides a snapshot of timing values.</param>
protected override void Update(GameTime gameTime)
{
testRot += 0.034906585f;
// Allows the game to exit
if (GamePad.GetState(PlayerIndex.One).Buttons.Back == ButtonState.Pressed)
this.Exit();
UpdateAsteroid(gameTime);
RotateShip(gameTime);
MoveShip(gameTime);
// TODO: Add your update logic here
CheckCollisions();
base.Update(gameTime);
}
#region Collisions
public Color PixelColor(int objectNum, int pixelNum)
{
switch (objectNum)
{
case rock:
return rockColor[pixelNum];
case ship:
return shipColor[pixelNum];
}
return Color.White;
}
public bool PixelCollision(Matrix transformA, int pixelWidthA, int pixelHeightA, int A,
Matrix transformB, int pixelWidthB, int pixelHeightB, int B)
{
Matrix temp = Matrix.Invert(transformB);
Matrix AtoB = transformA * Matrix.Invert(transformB);
Vector2 columnStep, rowStep, rowStartPosition;
columnStep = Vector2.TransformNormal(Vector2.UnitX, AtoB);
rowStep = Vector2.TransformNormal(Vector2.UnitY, AtoB);
rowStartPosition = Vector2.Transform(Vector2.Zero, AtoB);
for (int rowA = 0; rowA < pixelHeightA; rowA++)
{
// begin at the left
Vector2 pixelPositionA = rowStartPosition;
// for each column in the row (move left to right)
for (int colA = 0; colA < pixelWidthA; colA++)
{
// get the pixel position
int X = (int)Math.Round(pixelPositionA.X);
int Y = (int)Math.Round(pixelPositionA.Y);
// if the pixel is within the bounds of B
if (X >= 0 && X < pixelWidthB && Y >= 0 && Y < pixelHeightB)
{
// get colors of overlapping pixels
Color colorA = PixelColor(A, colA + rowA * pixelWidthA);
Color colorB = PixelColor(B, X + Y * pixelWidthB);
// if both pixels are not completely transparent,
if (colorA.A != 0 && colorB.A != 0)
return true; // collision
}
// move to the next pixel in the row of A
pixelPositionA += columnStep;
}
// move to the next row of A
rowStartPosition += rowStep;
}
return false; // no collision
}
public Matrix Transform(Vector2 center, float rotation, Vector2 position)
{
return Matrix.CreateTranslation(new Vector3(-center, 0.0f)) *
Matrix.CreateRotationZ(rotation) *
Matrix.CreateTranslation(new Vector3(position, 0.0f));
}
public static Rectangle TransformRectangle(Matrix transform, int width, int height)
{
Vector2 leftTop = new Vector2(0.0f, 0.0f);
Vector2 rightTop = new Vector2(width, 0.0f);
Vector2 leftBottom = new Vector2(0.0f, height);
Vector2 rightBottom = new Vector2(width, height);
Vector2.Transform(ref leftTop, ref transform, out leftTop);
Vector2.Transform(ref rightTop, ref transform, out rightTop);
Vector2.Transform(ref leftBottom, ref transform, out leftBottom);
Vector2.Transform(ref rightBottom, ref transform, out rightBottom);
Vector2 min = Vector2.Min(Vector2.Min(leftTop, rightTop), Vector2.Min(leftBottom, rightBottom));
Vector2 max = Vector2.Max(Vector2.Max(leftTop, rightTop), Vector2.Max(leftBottom, rightBottom));
return new Rectangle((int)min.X, (int)min.Y,
(int)(max.X - min.X), (int)(max.Y - min.Y));
}
private void CheckCollisions()
{
Matrix shipTransform, rockTransform;
Rectangle shipRectangle, rockRectangle;
rockTransform = Transform(rockCenter, rockRotation, rockPosition);
rockRectangle = TransformRectangle(rockTransform, rockWidth, rockHeight);
shipTransform = Transform(shipCenter, shipRotation, shipPosition);
shipRectangle = TransformRectangle(shipTransform, shipWidth, shipHeight);
if (rockRectangle.Intersects(shipRectangle)) // rough collision check
if (PixelCollision( // exact collision check
rockTransform, rockWidth, rockHeight, rock,
shipTransform, shipWidth, shipHeight, ship))
move = false;
}
#endregion
#region Moves_and_Rotations
private void UpdateAsteroid(GameTime gameTime)
{
float timeLapse = (float)gameTime.ElapsedGameTime.Milliseconds;
if (move == true)
{
if ((rockWidth + rockPosition.X >= Window.ClientBounds.Width))
{
rockSpeed *= -1.0f;
rockPosition.X += rockSpeed * timeLapse;
}
else if ((rockPosition.X <= 0))
{
rockSpeed *= -1.0f;
rockPosition.X += rockSpeed * timeLapse;
}
else
rockPosition.X += rockSpeed * timeLapse;
const float SCALE = 50.0f;
rockRotation += rockRotationSpeed * timeLapse / SCALE;
rockRotation = rockRotation % (MathHelper.Pi * 2.0f);
}
}
private float RotateShip(GameTime gameTime)
{
float rotation = 0.0f;
float speed = gameTime.ElapsedGameTime.Milliseconds / 300.0f;
if (!move)
return rotation;
KeyboardState keyboard = Keyboard.GetState();
if (keyboard.IsKeyDown(Keys.Right))
rotation = speed;
else if (keyboard.IsKeyDown(Keys.Left))
rotation = -speed;
shipRotation += rotation;
shipRotation = shipRotation % (MathHelper.Pi * 2.0f);
return shipRotation;
}
private void MoveShip(GameTime gameTime)
{
const float SCALE = 20.0f;
float speed = gameTime.ElapsedGameTime.Milliseconds / 100.0f;
KeyboardState keyboard = Keyboard.GetState();
if (keyboard.IsKeyDown(Keys.Up))
{
shipPosition.X += (float)Math.Sin(shipRotation) * speed * SCALE;
shipPosition.Y -= (float)Math.Cos(shipRotation) * speed * SCALE;
}
else if (keyboard.IsKeyDown(Keys.Down))
{
shipPosition.X -= (float)Math.Sin(shipRotation) * speed * SCALE;
shipPosition.Y += (float)Math.Cos(shipRotation) * speed * SCALE;
}
}
#endregion
}
我从XNA游戏创作者那里得到了它,它只是一种做像素检测的方法.
在上面的Transform方法中,矩阵乘法发生在我猜一个矩形.在屏幕空间/世界空间方面究竟发生了什么？
为什么作者将矩阵乘以另一个矩阵的倒数？(他提到不知何故,这使得它与其他资产相关)
屏幕空间可能与Client Space相同.客户端空间从左上角的(0,0)到右下角的(宽度,高度)."向上"是Y-.
投影空间从左下角的(-1,-1)变为右上角的(1,1).这是GPU用于最终渲染的内容.SpriteBatch为您处理此问题(相比之下:BasicEffect要求您提供投影矩阵).
世界空间是你想要的.这是您的游戏玩法所发生的坐标系.在您的示例中,它似乎与客户端空间相同.
传统上,在执行此类操作时,您在自己的空间中定义了一个对象.在你的榜样岩石和船舶矩形被硬编码到函数TransformRectangle的变量的初始值topLeft通过bottomRight.
然后,每个对象都有一个World矩阵.这将该对象从其自己的空间移动到其在世界空间中的位置.在你的例子中,这是shipTransform和rockTransform.基于您传入的参数(使用纹理本身作为初始对象),也可以在内部完成World变换SpriteBatch.Draw.
然后你有一个View矩阵 - 你可以把它想象成你的相机.您的示例没有其中之一.但是,如果您想要平移视图以跟随播放器,您可以在此处使用转换矩阵,从播放器的位置创建(并传递给它SpriteBatch.Begin).
最后你有一个Projection矩阵,可以将你的世界空间转换为投影空间,以便GPU可以渲染你的场景.
现在一个可能的问题是SpriteBatch在内部定义了一个投影矩阵,它将客户空间转换为投影空间(因此它基本上"假设"世界空间是客户空间).在您的示例中不是问题,因为两个空格是相同的.
如果你的世界空间是不一样的东西客户端的空间,并要使用SpriteBatch,你必须创建一个额外的矩阵,从世界空间转换到客户空间和景观和项目矩阵之间插入(即:与浏览乘以并传递给SpriteBatch.Begin).
如果你的世界空间定义了与SpriteBatch不同的"向上"(或"右")方式,那么你必须记住SpriteBatch.Draw定义"向上" 使用的原始对象是Y-.
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