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Using quaternions for rotations - dynamically positioning the camera behind our xwing |
Imagine our xwing would be flying through our 3D city. We would like our camera to always follow our xwing, so the camera would always be positioned behind the xwing, no matter which rotation of translation our xwing has.
First we're going to introduce 2 new variables, xwingPosition and xwingRotationg. These variables will determine the position of our camera, as the position of the camera needs to change as our xwing moves/rotates.
We could store the rotation of our xwing as separate rotations around the X, Y and Z axis. However, in practice this is very tricky. The problem is mainly the same as with matrices: a rotation around X followed by a rotation around Y does NOT yield the same as a rotation around Y followed by a rotation around X. Recipe 4-2 explains the cause of these problems.
In addition, deriving the total rotation from 3 separate values requires some trigonometric formulae (sin, cos, tan,…). Sometimes, these suddenly switch signs, what would make our xwing to fly backwards.
To solve both problems, we’ll be using a Quaternion to store the rotation of our xwing. A Quaternion is much like a Matrix, but can only store a rotation. Don’t let the name of this thing scare you away: although it’s very hard to understand mathematically, a quaternion is VERY easy to use. Go ahead and declare these 2 variables at the top of your code:
Vector3 xwingPosition = new Vector3(8, 1, -3);
Quaternion xwingRotation = Quaternion.Identity;
As you can see, we’ve already initialized a starting position and rotation for our xwing. Next chapter we’ll see how we can adjust the quaternion based on user input, for now use the unity quaternion.
To accomplish the goal of this chapter, we will draw the 3D city, then draw the xwing at its correct position and rotation, and then reposition the camera immediately behind our airplane.
In our DrawModel method, we can already change the world matrix for our xwing, so it’s drawn at the correct location, and with the correct rotation:
Matrix worldMatrix = Matrix.CreateScale(0.0005f, 0.0005f, 0.0005f) * Matrix.CreateRotationY(MathHelper.Pi) * Matrix.CreateFromQuaternion(xwingRotation) * Matrix.CreateTranslation(xwingPosition);
This line looks complex, but it’s quite easy: first the model is scaled down so it fits nicely in our scene, and it is rotated along 180 degrees in the correct direction to begin with.
New to this chapter, the xwing is rotated among the rotation stored in the xwingRotation quaternion. Here you can already notice how easy it is to retrieve the rotation matrix corresponding to a quaternion. Finally, the mesh is translated (=moved) to its correct position.
Now we have our xwing at the correct position and correctly rotated, it’s time to position the camera behind the xwing. We’re going to create a method to do this. So our method will create a new viewMatrix and projectionMatrix that depend on the current position and rotation of the xwing. Let’s start with this:
private void UpdateCamera()
{
Vector3 campos = new Vector3(0, 0.1f, 0.6f);
}
This vector will define where we want our camera to be, relative to the position of the xwing: we want to position the camera a bit behind (Z=+0.6f)and above (Y=+0.1f) our xwing, so the vector only has a Y and Z component. This vector still needs to be transformed: it needs to be translated (=moved) to the position of our mesh, and then it needs to be rotated with the rotation of the xwing, so it end up nicely behind the xwing.
You can find a detailed explanation about this approach in Recipe 2-4.
Let’s first process the rotation transform:
campos = Vector3.Transform(campos, Matrix.CreateFromQuaternion(xwingRotation));
Now the campos variable holds the vector that will always be behind (and a bit above) our xwing no matter what its rotation is, IF the xwing is in the (0,0,0) position. Because the position of our xwing will constantly change, we need to move (=translate) our campos vector to the position of our xwing, which is done using the following line:
campos += xwingPosition;
OK, so now we have the vector that will always be a bit behind and a bit above our xwing, no matter which rotation and/or translation our xwing has!
Remember, when we create a viewMatrix, we not only need the position and target of our camera (which we both know at this moment), but also the vector that indicates the ‘up’-position of the xwing. This is found exactly the same way: we start with the vector that points up, and rotate it with the xwing rotation matrix:
Vector3 camup = new Vector3(0, 1, 0);
camup = Vector3.Transform(camup, Matrix.CreateFromQuaternion(xwingRotation));
Now we have everything to create our camera matrices: the position, target and up-vector, so we can create our new matrices:
viewMatrix = Matrix.CreateLookAt(campos, xwingPosition, camup);
projectionMatrix = Matrix.CreatePerspectiveFieldOfView(MathHelper.PiOver4, device.Viewport.AspectRatio, 0.2f, 500.0f);
Only the first line contains the newly created vectors, the second line has remained the same.
Quite a method, let’s make sure we call it from the Update method:
protected override void Update(GameTime gameTime)
{
UpdateCamera();
base.Update(gameTime);
}
That’s it! When you run this code, you’ll see the camera has been positioned behind and above your xwing, as on the image below:
Click here to go to the forum on this chapter!
Or click on one of the topics on this chapter to go there:
Chase Camera
I cannot get the chase camera to follow my ship. ...camup variable
Hi,
somebody could explain what's the meaning ...Positionning the camera in the cockpit
Hi
in number of games we can set the camera in...Inverting the camera
Hi,
I have been following the tuts and I´m a bi...
Now we have our code ready so it adjust the xwing and camera to the spacemeshposition and spacemeshrotation variable, it’s time to read out the keyboard. Anyway, we now have a dynamic camera that follows our xwing, no matter what its position and rotation is.
You can try these exercises to practice what you've learned:
Change the position of the xwing, you’ll see that the camera follows!
The code:
using System;
using System.Collections.Generic;
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Audio;
using Microsoft.Xna.Framework.Content;
using Microsoft.Xna.Framework.GamerServices;
using Microsoft.Xna.Framework.Graphics;
using Microsoft.Xna.Framework.Input;
using Microsoft.Xna.Framework.Net;
using Microsoft.Xna.Framework.Storage;
namespace XNAseries2
{
public class Game1 : Microsoft.Xna.Framework.Game
{
int[] buildingHeights = new int[] { 0, 2, 2, 6, 5, 4 };
GraphicsDeviceManager graphics;
GraphicsDevice device;
Effect effect;
Vector3 lightDirection = new Vector3(3, -2, 5);
Matrix viewMatrix;
Matrix projectionMatrix;
Texture2D sceneryTexture;
Model xwingModel;
Vector3 xwingPosition = new Vector3(8, 1, -3);
Quaternion xwingRotation = Quaternion.Identity;
int[,] floorPlan;
VertexBuffer cityVertexBuffer;
VertexDeclaration texturedVertexDeclaration;
public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = "Content";
}
protected override void Initialize()
{
graphics.PreferredBackBufferWidth = 500;
graphics.PreferredBackBufferHeight = 500;
graphics.IsFullScreen = false;
graphics.ApplyChanges();
Window.Title = "Riemer's XNA Tutorials -- Series 2";
LoadFloorPlan();
lightDirection.Normalize();
base.Initialize();
}
protected override void LoadContent()
{
device = graphics.GraphicsDevice;
effect = Content.Load<Effect>
("effects");
sceneryTexture = Content.Load<Texture2D>
("texturemap");
xwingModel = LoadModel("xwing");
SetUpVertices();
SetUpCamera();
}
private Model LoadModel(string assetName)
{
Model newModel = Content.Load<Model>
(assetName); foreach (ModelMesh mesh in newModel.Meshes)
foreach (ModelMeshPart meshPart in mesh.MeshParts)
meshPart.Effect = effect.Clone(device);
return newModel;
}
private void LoadFloorPlan()
{
floorPlan = new int[,]
{
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,1,1,0,0,0,1,1,0,0,1,0,1},
{1,0,0,1,1,0,0,0,1,0,0,0,1,0,1},
{1,0,0,0,1,1,0,1,1,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,1,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,1,1,0,0,0,1,0,0,0,0,0,0,1},
{1,0,1,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,1,0,0,0,0,0,0,0,0,1},
{1,0,0,0,0,1,0,0,0,1,0,0,0,0,1},
{1,0,1,0,0,0,0,0,0,1,0,0,0,0,1},
{1,0,1,1,0,0,0,0,1,1,0,0,0,1,1},
{1,0,0,0,0,0,0,0,1,1,0,0,0,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
};
Random random = new Random();
int differentBuildings = buildingHeights.Length - 1;
for (int x = 0; x < floorPlan.GetLength(0); x++)
for (int y = 0; y < floorPlan.GetLength(1); y++)
if (floorPlan[x, y] == 1)
floorPlan[x, y] = random.Next(differentBuildings) + 1;
}
private void SetUpCamera()
{
viewMatrix = Matrix.CreateLookAt(new Vector3(20, 13, -5), new Vector3(8, 0, -7), new Vector3(0, 1, 0));
projectionMatrix = Matrix.CreatePerspectiveFieldOfView(MathHelper.PiOver4, device.Viewport.AspectRatio, 0.2f, 500.0f);
}
private void SetUpVertices()
{
int differentBuildings = buildingHeights.Length - 1;
float imagesInTexture = 1 + differentBuildings * 2;
int cityWidth = floorPlan.GetLength(0);
int cityLength = floorPlan.GetLength(1);
List<VertexPositionNormalTexture>
verticesList = new List<VertexPositionNormalTexture>
();
for (int x = 0; x < cityWidth; x++)
{
for (int z = 0; z < cityLength; z++)
{
int currentbuilding = floorPlan[x, z];
//floor or ceiling
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z), new Vector3(0, 1, 0), new Vector2(currentbuilding * 2 / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 1, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z), new Vector3(0, 1, 0), new Vector2((currentbuilding * 2 + 1) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 1, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 1, 0), new Vector2((currentbuilding * 2 + 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z), new Vector3(0, 1, 0), new Vector2((currentbuilding * 2 + 1) / imagesInTexture, 1)));
if (currentbuilding != 0)
{
//front wall
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, 0, -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z - 1), new Vector3(0, 0, -1), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
//back wall
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, 0, -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z), new Vector3(0, 0, 1), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
//left wall
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, 0, -z), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, 0, -z - 1), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z - 1), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, buildingHeights[currentbuilding], -z), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x, 0, -z), new Vector3(-1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
//right wall
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z - 1), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z - 1), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z - 1), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2 - 1) / imagesInTexture, 0)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, 0, -z), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 1)));
verticesList.Add(new VertexPositionNormalTexture(new Vector3(x + 1, buildingHeights[currentbuilding], -z), new Vector3(1, 0, 0), new Vector2((currentbuilding * 2) / imagesInTexture, 0)));
}
}
}
cityVertexBuffer = new VertexBuffer(device, verticesList.Count * VertexPositionNormalTexture.SizeInBytes, BufferUsage.WriteOnly);
cityVertexBuffer.SetData<VertexPositionNormalTexture>
(verticesList.ToArray());
texturedVertexDeclaration = new VertexDeclaration(device, VertexPositionNormalTexture.VertexElements);
}
protected override void UnloadContent()
{
}
protected override void Update(GameTime gameTime)
{
UpdateCamera();
base.Update(gameTime);
}
private void UpdateCamera()
{
Vector3 campos = new Vector3(0, 0.1f, 0.6f);
campos = Vector3.Transform(campos, Matrix.CreateFromQuaternion(xwingRotation));
campos += xwingPosition;
Vector3 camup = new Vector3(0, 1, 0);
camup = Vector3.Transform(camup, Matrix.CreateFromQuaternion(xwingRotation));
viewMatrix = Matrix.CreateLookAt(campos, xwingPosition, camup);
projectionMatrix = Matrix.CreatePerspectiveFieldOfView(MathHelper.PiOver4, device.Viewport.AspectRatio, 0.2f, 500.0f);
}
protected override void Draw(GameTime gameTime)
{
device.Clear(ClearOptions.Target | ClearOptions.DepthBuffer, Color.DarkSlateBlue, 1.0f, 0);
DrawCity();
DrawModel();
base.Draw(gameTime);
}
private void DrawCity()
{
effect.CurrentTechnique = effect.Techniques["Textured"];
effect.Parameters["xWorld"].SetValue(Matrix.Identity);
effect.Parameters["xView"].SetValue(viewMatrix);
effect.Parameters["xProjection"].SetValue(projectionMatrix);
effect.Parameters["xTexture"].SetValue(sceneryTexture);
effect.Parameters["xEnableLighting"].SetValue(true);
effect.Parameters["xLightDirection"].SetValue(lightDirection);
effect.Parameters["xAmbient"].SetValue(0.5f);
effect.Begin();
foreach (EffectPass pass in effect.CurrentTechnique.Passes)
{
pass.Begin();
device.VertexDeclaration = texturedVertexDeclaration;
device.Vertices[0].SetSource(cityVertexBuffer, 0, VertexPositionNormalTexture.SizeInBytes);
device.DrawPrimitives(PrimitiveType.TriangleList, 0, cityVertexBuffer.SizeInBytes / VertexPositionNormalTexture.SizeInBytes / 3);
pass.End();
}
effect.End();
}
private void DrawModel()
{
Matrix worldMatrix = Matrix.CreateScale(0.0005f, 0.0005f, 0.0005f) * Matrix.CreateRotationY(MathHelper.Pi) * Matrix.CreateFromQuaternion(xwingRotation) * Matrix.CreateTranslation(xwingPosition);
Matrix[] xwingTransforms = new Matrix[xwingModel.Bones.Count];
xwingModel.CopyAbsoluteBoneTransformsTo(xwingTransforms);
foreach (ModelMesh mesh in xwingModel.Meshes)
{
foreach (Effect currentEffect in mesh.Effects)
{
currentEffect.CurrentTechnique = currentEffect.Techniques["Colored"];
currentEffect.Parameters["xWorld"].SetValue(xwingTransforms[mesh.ParentBone.Index] * worldMatrix);
currentEffect.Parameters["xView"].SetValue(viewMatrix);
currentEffect.Parameters["xProjection"].SetValue(projectionMatrix);
currentEffect.Parameters["xEnableLighting"].SetValue(true);
currentEffect.Parameters["xLightDirection"].SetValue(lightDirection);
currentEffect.Parameters["xAmbient"].SetValue(0.5f);
}
mesh.Draw();
}
}
}
}
- Website design & XNA + DirectX code : Riemer Grootjans -
©2003 - 2008 Riemer Grootjans
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