Develop Reference

Creating a Google Earth like navigation for a sphere

This question is about Unity3D.
I want to create a navigation similar to Google Earth where you click and drag on a sphere and let the camera orbit accordingly. It is important that the point that was grabbed is always under the mouse position while dragging. The navigation should also work if I zoom close to the sphere. I do not want to rotate the sphere itself. Just exactly like Google Earth does it.
My attempt is to project the mouse position to the sphere if I start to drag. On the next frame I do the same and calculate the angle between the start drag and end drag position.
private void RotateCamera(Vector3 dragStart, Vector3 dragEnd)
{
// calc the rotation of the drag
float angle = Vector3.Angle(dragStart, dragEnd);
// rotate the camera around the sphere
Camera.main.transform.RotateAround(sphere), Vector3.up, angle);
}
I thought of using Unitys RotateAround method to rotate the camera with the calculated angle. Unfortunately I do not have the rotation vector (using Vector3.up in the example is obviously wrong).
Does somebody know how I can calculate this vector to apply it for the method? Am I on the right direction to implement the Google Earth navigation?
Thank You!
UPDATE
I am very close with a new solution. I project the drag vectors to a down and a right plane to get the angles. Afterwards I rotate the camera around up and left. This works well until I reach the poles of the sphere. The camera rotates a lot around itself if I reach a pole.
private void RotateCamera(Vector3 dragStart, Vector3 dragEnd)
{
Vector3 plane = Vector3.down;
var a = Vector3.ProjectOnPlane(dragStart, plane);
var b = Vector3.ProjectOnPlane(dragEnd, plane);
float up = Vector3.SignedAngle(a, b, plane);
plane = Vector3.right;
a = Vector3.ProjectOnPlane(dragStart, plane);
b = Vector3.ProjectOnPlane(dragEnd, plane);
float left = Vector3.SignedAngle(a, b, plane);
Camera.main.transform.RotateAround(_sphere, Vector3.up, up);
Camera.main.transform.RotateAround(_sphere, Vector3.left, left);
}

Turns out that is was easier than I expected. I thought about calculating the rotation axis and came to the conclusion that is must be the cross product of the start and end vector. Take a look at the solution. The RotateCamera method is where the math magic happens :)
public class GoogleEarthControls : MonoBehaviour
{
private const int SpehreRadius = 1;
private Vector3? _mouseStartPos;
private Vector3? _currentMousePos;
void Start () {
// init the camera to look at this object
Vector3 cameraPos = new Vector3(
transform.position.x,
transform.position.y,
transform.position.z - 2);
Camera.main.transform.position = cameraPos;
Camera.main.transform.LookAt(transform.position);
}
private void Update()
{
if (Input.GetMouseButtonDown(0)) _mouseStartPos = GetMouseHit();
if (_mouseStartPos != null) HandleDrag();
if (Input.GetMouseButtonUp(0)) HandleDrop();
}
private void HandleDrag()
{
_currentMousePos = GetMouseHit();
RotateCamera((Vector3) _mouseStartPos, (Vector3)_currentMousePos);
}
private void HandleDrop()
{
_mouseStartPos = null;
_currentMousePos = null;
}
private void RotateCamera(Vector3 dragStartPosition, Vector3 dragEndPosition)
{
// in case the spehre model is not a perfect sphere..
dragEndPosition = dragEndPosition.normalized * SpehreRadius;
dragStartPosition = dragStartPosition.normalized * SpehreRadius;
// calc a vertical vector to rotate around..
var cross = Vector3.Cross(dragEndPosition, dragStartPosition);
// calc the angle for the rotation..
var angle = Vector3.SignedAngle(dragEndPosition, dragStartPosition, cross);
// roatate around the vector..
Camera.main.transform.RotateAround(transform.position, cross, angle);
}
/**
* Projects the mouse position to the sphere and returns the intersection point.
*/
private static Vector3? GetMouseHit()
{
// make sure there is a shepre mesh with a colider centered at this game object
// with a radius of SpehreRadius
RaycastHit hit;
if (Physics.Raycast(Camera.main.ScreenPointToRay(Input.mousePosition), out hit))
{
return hit.point;
}
return null;
}
}

Basic rotation based on mouse drag, based on what you have:
Transform camTransform = Camera.main.transform;
if (Input.GetMouseButton(0))
{
camTransform.RotateAround(currentLookTargetTransform.position, -camTransform.right * Input.GetAxis("Mouse Y") + camTransform.up * Input.GetAxis("Mouse X"), 120 * Time.deltaTime);
}
You can multiply the relative direction by the mouse change value to get the axis. Then you can supplant your clamp points in; but the point was to rotate it relatively.

XNA-Moving rotated camera(view) relative to world

So I've been trying to get this to work but no luck so far, hopefully you can help. The thing is I have a camera in my project that the user can freely move with mouse and buttons.
Currently like so:
move = new Vector3(0, 0, -1) * moveSpeed;
move = new Vector3(0, 0, 1) * moveSpeed;
...
And then I just add move vector to cameraPos vector: cameraPos += move
Then problem is if I rotate the camera and then try to move, for example down, it will not move straight down but in a certain angle. I am assuming this is due to moving on local axis. But what I want to do is to move on a world axis. Is something like that possible, or do I have to somehow calculate the angle and then move on more than one axis?
Best regards!
EDIT:
I am rotating the camera where cameraPos is the current position of the camera and rotation is the current rotation of the camera. And this is the code to rotate the camera:
void Update()
{
...
if(pressed)
{
int newY = currentY - oldY;
pitch -= rotSpeed * newY;
}
Rotate();
}
void Rotate()
{
rotation = Matrix.CreateRotationX(pitch);
Vector3 transformedReference = Vector3.Transform(cameraPos, rotation);
Vector3 lookAt = cameraPos + transformedReference;
view = Matrix.CreateLookAt(cameraPos, lookAt, Vector3.Up);
oldY = currentY;
}
Ihope this is more readable.

I was able to solve this problem by using:
Vector3 v;
if (state.IsKeyDown(Keys.Up))
v = new Vector3(0, 0, 1) * moveSpeed;
... //Other code for moving down,left,right
if (state.IsKeyDown(Keys.V))
view *= Matrix.CreateRotationX(MathHelper.ToRadians(-5f) * rotSpeed); //Multiplying view Matrix to create rotation
view *= Matrix.CreateTranslation(v); //Multiplying view Matrix to create movement by Vector3 v

I suppose you're already saving the direction you're looking at in a Vector3. Replace your method with this:
direction.Normalize();
var move = direction * moveSpeed;
cameraPos += move;

Only seeing 1 object out of an array of 3 in XNA

Can anyone see where I am going wrong here.
I have a CameraObject class (its not a camera, simply the Model of a box to represent a "camera") that has a Model and a Position. It also has the usual LoadContent(), Draw() and Update() methods.
However, when I draw the array of Models, I only see 1 model on the screen (well, there might be 3 but they might all be in the same location)?
The Draw() method for the CameraModel class looks like this:
public void Draw(Matrix view, Matrix projection)
{
transforms = new Matrix[CameraModel.Bones.Count];
CameraModel.CopyAbsoluteBoneTransformsTo(transforms);
// Draw the model
foreach(ModelMesh myMesh in CameraModel.Meshes)
{
foreach (BasicEffect myEffect in myMesh.Effects)
{
myEffect.World = transforms[myMesh.ParentBone.Index];
myEffect.View = view;
myEffect.Projection = projection;
myEffect.EnableDefaultLighting();
myEffect.SpecularColor = new Vector3(0.25f);
myEffect.SpecularPower = 16;
}
myMesh.Draw();
}
}
Then in my Game1 class I create an array of CameraObject objects:
CameraObject[] cameraObject = new CameraObject[3];
Which I Initialize() - so each new object should be at +10 from the previous object
for (int i = 0; i < cameraObject.Length; i++)
{
cameraObject[i] = new CameraObject();
cameraObject[i].Position = new Vector3(i * 10, i * 10, i * 10);
}
And finally Draw()
Matrix view = camera.viewMatrix;
Matrix projection = camera.projectionMatrix;
for (int i = 0; i < cameraObject.Length; i++)
{
cameraObject[i].Draw(view, projection);
}
Where view and projection are from my Camera() class which looks like so:
viewMatrix = Matrix.Identity;
projectionMatrix = Matrix.CreatePerspectiveFieldOfView(MathHelper.ToRadians(45.0f), 16 / 9, .5f, 500f);
But I only see 1 object drawn to the screen? I have stepped through the code and all seems well but I cant figure out why I cant see 3 objects?
Can anyone spot where I am going wrong?
This is the code in my Camera() class to UpdateViewMatrix:
private void UpdateViewMatrix(Matrix chasedObjectsWorld)
{
switch (currentCameraMode)
{
case CameraMode.free:
// To be able to rotate the camera and and not always have it looking at the same point
// Normalize the cameraRotation’s vectors, as those are the vectors that the camera will rotate around
cameraRotation.Forward.Normalize();
cameraRotation.Up.Normalize();
cameraRotation.Right.Normalize();
// Multiply the cameraRotation by the Matrix.CreateFromAxisAngle() function,
// which rotates the matrix around any vector by a certain angle
// Rotate the matrix around its own vectors so that it works properly no matter how it’s rotated already
cameraRotation *= Matrix.CreateFromAxisAngle(cameraRotation.Right, pitch);
cameraRotation *= Matrix.CreateFromAxisAngle(cameraRotation.Up, yaw);
cameraRotation *= Matrix.CreateFromAxisAngle(cameraRotation.Forward, roll);
// After the matrix is rotated, the yaw, pitch, and roll values are set back to zero
yaw = 0.0f;
pitch = 0.0f;
roll = 0.0f;
// The target is changed to accommodate the rotation matrix
// It is set at the camera’s position, and then cameraRotation’s forward vector is added to it
// This ensures that the camera is always looking in the direction of the forward vector, no matter how it’s rotated
target = Position + cameraRotation.Forward;
break;
case CameraMode.chase:
// Normalize the rotation matrix’s forward vector because we’ll be using that vector to roll around
cameraRotation.Forward.Normalize();
chasedObjectsWorld.Right.Normalize();
chasedObjectsWorld.Up.Normalize();
cameraRotation = Matrix.CreateFromAxisAngle(cameraRotation.Forward, roll);
// Each frame, desiredTarget will be set to the position of whatever object we’re chasing
// Then set the actual target equal to the desiredTarget, can then change the target’s X and Y coordinates at will
desiredTarget = chasedObjectsWorld.Translation;
target = desiredTarget;
target += chasedObjectsWorld.Right * yaw;
target += chasedObjectsWorld.Up * pitch;
// Always want the camera positioned behind the object,
// desiredPosition needs to be transformed by the chased object’s world matrix
desiredPosition = Vector3.Transform(offsetDistance, chasedObjectsWorld);
// Smooth the camera’s movement and transition the target vector back to the desired target
Position = Vector3.SmoothStep(Position, desiredPosition, .15f);
yaw = MathHelper.SmoothStep(yaw, 0f, .1f);
pitch = MathHelper.SmoothStep(pitch, 0f, .1f);
roll = MathHelper.SmoothStep(roll, 0f, .1f);
break;
case CameraMode.orbit:
// Normalizing the rotation matrix’s forward vector, and then cameraRotation is calculated
cameraRotation.Forward.Normalize();
// Instead of yawing and pitching over cameraRotation’s vectors, we yaw and pitch over the world axes
// By rotating over world axes instead of local axes, the orbiting effect is achieved
cameraRotation = Matrix.CreateRotationX(pitch) * Matrix.CreateRotationY(yaw) * Matrix.CreateFromAxisAngle(cameraRotation.Forward, roll);
desiredPosition = Vector3.Transform(offsetDistance, cameraRotation);
desiredPosition += chasedObjectsWorld.Translation;
Position = desiredPosition;
target = chasedObjectsWorld.Translation;
roll = MathHelper.SmoothStep(roll, 0f, .2f);
break;
}
// Use this line of code to set up the View Matrix
// Calculate the view matrix
// The up vector is based on how the camera is rotated and not off the standard Vector3.Up
// The view matrix needs an up vector to fully orient itself in 3D space, otherwise,
// the camera would have no way of knowing whether or not it’s upside-down
viewMatrix = Matrix.CreateLookAt(Position, target, cameraRotation.Up);
}

I'm not seeing in your code where your cameraObject[n].Position (which is probably the only thing that uniquely differentiates the position between the three models) is affecting the effect.World property.
effect.World = transforms[myMesh.ParentBone.Index];
does not typically take individual model position into account.
Try something like this:
for (int i = 0; i < cameraObject.Length; i++)
{
cameraObject[i].Draw(view, projection, cameraObject[i].Position);
}
//later in the draw method
public void Draw(Matrix view, Matrix projection, Vector3 pos)
{
// ...
myEffect.World = transforms[myMesh.ParentBone.Index] * Matrix.CreateTranslation(pos);
// ...
}

CameraObject[1] & [2] are located at a greater positive Z value than camera[0] and the view matrix is located at the origin & looking in a negative Z direction (remember, the view matrix is the inverted equivalent of a world matrix).
Instead of setting your viewMatrix to Matrix.Identity, set it to this and you might see all three:
viewMatrix = Matrix.CreateLookAt(new Vector3(0,0,75), Vector3.Zero, Vector3.Up);

control a spaceship in 3 axes in XNA

when i control the spaceship in 1 axis all is fine, that is, the depth(z) and the rotation on the z plane 360 degrees, so thats 2 axis. I also have a camera right behind it which i have to maintain its position. When the 3rd comes in place all go bad. let me show you some code:
Here is the part that fails:
draw method of spaceship :
public void Draw(Matrix view, Matrix projection)
{
public float ForwardDirection { get; set; }
public float VerticalDirection { get; set; }
Matrix[] transforms = new Matrix[Model.Bones.Count];
Model.CopyAbsoluteBoneTransformsTo(transforms);
Matrix worldMatrix = Matrix.Identity;
Matrix worldMatrix2 = Matrix.Identity;
Matrix rotationYMatrix = Matrix.CreateRotationY(ForwardDirection);
Matrix rotationXMatrix = Matrix.CreateRotationX(VerticalDirection); // me
Matrix translateMatrix = Matrix.CreateTranslation(Position);
worldMatrix = rotationYMatrix * translateMatrix;
worldMatrix2 = rotationXMatrix * translateMatrix;
//worldMatrix*= rotationXMatrix;
foreach (ModelMesh mesh in Model.Meshes) //NEED TO FIX THIS
{
foreach (BasicEffect effect in mesh.Effects)
{
effect.World =
worldMatrix * transforms[mesh.ParentBone.Index]; ; //position
//effect.World =
//worldMatrix2 * transforms[mesh.ParentBone.Index]; ; //position
effect.View = view; //camera
effect.Projection = projection; //2d to 3d
effect.EnableDefaultLighting();
effect.PreferPerPixelLighting = true;
}
mesh.Draw();
}
}
For the extra axis the worldMatrix2 is implemented which i DONT know how to combine with the other axis. Do i multiply it? Also:
The camera update method has a similar problem:
public void Update(float avatarYaw,float avatarXaw, Vector3 position, float aspectRatio)
{
//Matrix rotationMatrix = Matrix.CreateRotationY(avatarYaw);
Matrix rotationMatrix2 = Matrix.CreateRotationX(avatarXaw);
//Vector3 transformedheadOffset =
//Vector3.Transform(AvatarHeadOffset, rotationMatrix);
Vector3 transformedheadOffset2 = Vector3.Transform(AvatarHeadOffset, rotationMatrix2);
//Vector3 transformedheadOffset2 = Vector3.Transform(transformedheadOffset, rotationMatrix2);
//Vector3 transformedReference =
//Vector3.Transform(TargetOffset, rotationMatrix);
Vector3 transformedReference2 = Vector3.Transform(TargetOffset, rotationMatrix2);
//Vector3 transformedReference2 = Vector3.Transform(transformedReference, rotationMatrix2);
Vector3 cameraPosition = position + transformedheadOffset2; /** + transformedheadOffset; */
Vector3 cameraTarget = position + transformedReference2; /** + transformedReference; */
//Calculate the camera's view and projection
//matrices based on current values.
ViewMatrix =
Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up);
ProjectionMatrix =
Matrix.CreatePerspectiveFieldOfView(
MathHelper.ToRadians(GameConstants.ViewAngle), aspectRatio,
GameConstants.NearClip, GameConstants.FarClip);
}
}
Lastly here is the method of the Game class Update:
spaceship.Update(currentGamePadState,
currentKeyboardState); // this will be cahnged when asteroids are placed in the game, by adding a new parameter with asteroids.
float aspectRatio = graphics.GraphicsDevice.Viewport.AspectRatio;
gameCamera.Update(spaceship.ForwardDirection,spaceship.VerticalDirection,
spaceship.Position, aspectRatio);

Somewhere in your code, you probably have methodology that manipulates and sets the variables 'ForwardDirection' & 'VerticalDirection' which seem to represent angular values around the Y & X axis respectively. Presumably you may intend to have a variable that represents an angular value around the Z axis as well. I'm also assuming (and your code implies) that these variables are ultimately how you store your spaceship's orientation from frame to frame.
As long as you continue to try to represent an orientation using these angles, you will find it difficult to achieve the control of your spaceship.
There are several types of orientation representations available. The 3 angles approach has inherent weaknesses when it comes to combining rotations in 3 dimensions.
My recommendation is that you shift paradigms and consider storing and manipulating your orientations in a Matrix or a Quaternion form. Once you learn to manipulate a matrix or quaternion, what you are trying to do becomes almost unbelievably easy.

Direct3D 11 WorldViewProjection Matrix Transformation Not Working

I have a simple square I'm drawing in 3D space using Direct3D 11 and SlimDX, with the following coordinates (I know it renders)
0,0,0.5
0,0.5,0.5
0.5,0.5,0.5
0.5,0,0.5
I have a camera class that handles camera movement by applying matrix transformations to the viewmatrix. e.g. Camera.MoveForward(float x) moves the camera forward by x. It also holds the View and Projection matrices. I instantiate them using the following code:
Matrix view = Matrix.LookAtLH(
new Vector3(0f, 0f, -5f),
new Vector3(0f, 0f, 0f),
new Vector3(0f, 1f, 0f));
Matrix projection = Matrix.PerspectiveFovLH(
(float)Math.PI/2,
WINDOWWIDTH/WINDOWHEIGHT,
0.1f,
110f);
The world matrix is set to the identity matrix.
In my shader code I transform my coordinates using the following code:
PS_IN VS(VS_IN input)
{
PS_IN output = (PS_IN)0;
output.pos = mul( input.pos, WorldViewProjection );
output.col = float4(1,1,1,1);
return output;
}
Where WorldViewProjection is set in my code using the following:
Matrix worldview = Matrix.Multiply(world, camera.ViewMatrix);
Matrix worldviewprojection = Matrix.Multiply(worldview, camera.ProjectionMatrix);
I know the camera class's transformations are working as it's old code I wrote for an MDX application which worked fine, however when this runs I see my square, and moving forwards and backwards works just fine, but moving left and right seems to rotate the square around the Y (up) axis instead of translating it, moving up and down has a similar effect, rotating instead about the X (horizontal) axis.
For reference, the camera movement functions:
public void MoveRight(float distance)
{
position.Z += (float)(Math.Sin(-angle.Y) * -distance);
position.X += (float)(Math.Cos(-angle.Y) * -distance);
updateViewMatrix();
}
public void MoveForward(float distance)
{
position.X += (float)(Math.Sin(-angle.Y) * -distance);
position.Z += (float)(Math.Cos(-angle.Y) * -distance);
updateViewMatrix();
}
public void MoveUp(float distance)
{
position.Y -= distance;
updateViewMatrix();
}
private void updateViewMatrix()
{
ViewMatrix = Matrix.Translation(position.X, position.Y, position.Z) * Matrix.RotationY(angle.Y) * Matrix.RotationX(angle.X) * Matrix.RotationZ(angle.Z);
}

The issue may lie in the line:
output.pos = mul( input.pos, WorldViewProjection );
I would change output.pos to be a float4 and then do:
output.pos = mul( float4(input.pos, 1), WorldViewProjection );
Let me know how this works out. If this isn't the problem, I'll take a deeper look at what may be going on.