Changing the origin of a rotation matrix in XNA - matrix

I am trying to get 4 Vector2 objects representing the 4 corners of a sprite to rotate around the sprite itself rotates around its center. With my following code, however, the Vector2 objects rotate around 0,0 in Client Space instead of rotating around the center of the object. Using matrix transformations, is there any way to rotate the Vector2 objects around the center of the object instead of the global coordinate (0,0)?
Here is the function for the rotation so far:
public Vector2[] CheckCollision()
{
//Get the 4 corners of the sprite locally
//We can get all 4 corners from only 2 vectors
Vector2 topLeft = new Vector2(position.X - spriteSize.X, position.Y - spriteSize.Y);
//Not sure why position is representing the
//bottom right instead of the center here....
Vector2 bottomRight = position;
Vector2 bottomLeft = new Vector2(topLeft.X, bottomRight.Y);
Vector2 topRight = new Vector2(bottomRight.X, topLeft.Y);
//Create transformation matrix
Matrix transform = Matrix.CreateRotationZ(MathHelper.ToRadians(this.direction)) *
Matrix.CreateScale(this.scale);
//Transform the vectors
topLeft = Vector2.Transform(topLeft, transform);
bottomRight = Vector2.Transform(bottomRight, transform);
bottomLeft = Vector2.Transform(bottomLeft, transform);
topRight = Vector2.Transform(topRight, transform);
Vector2[] vectorArray = new Vector2[4];
vectorArray[0] = topLeft;
vectorArray[1] = bottomRight;
vectorArray[2] = bottomLeft;
vectorArray[3] = topRight;
return vectorArray;
}

It would probably be a lot easier to just rotate the four corners first before adding the spritePosition and add the spriteposition after the rotation and scaling has been performed.
Just make your four corners into the corresponding combinations of spriteSize and do the Vector2.Transform once that is done add the spritePosition to the four vectors in vectorArray

Related

Monogame - Rotate Sprite around centre of screen and itself

I have a problem and although I serached everywhere I couldn't find a solution.
I have a stacked sprite and I'm rotating this sprite around the center of the screen. So I iterate over a list of sprites (stacked) and increase the y-coordinate by 2 every loop (rotation is increased step by step by 0.01f outside of the loop):
foreach(var s in stacked)
{
Vector2 origin = new Vector2(Basic.width / 2, Basic.height / 2);
Rectangle newPosition = new Rectangle(position.X, position.Y - y, position.Width, position.Height);
float angle = 0f;
Matrix transform = Matrix.CreateTranslation(-origin.X, -origin.Y, 0f) *
Matrix.CreateRotationZ(rotation) *
Matrix.CreateTranslation(origin.X, origin.Y, 0f);
Vector2 pos = new Vector2(newPosition.X, newPosition.Y);
pos = Vector2.Transform(pos, transform);
newPosition.X = (int)pos.X;
newPosition.Y = (int)pos.Y;
angle += rotation;
s.Draw(newPosition, origin, angle, Color.White);
y += 2;
}
This works fine. But now my problem. I want not only to rotate the sprite around the center of the screen but also around itself. How to achieve this? I can only set one origin and one rotation per Draw. I would like to rotate the sprite around the origin 'Basic.width / 2, Basic.height / 2' and while it rotates, around 'position.Width / 2, position.Height / 2'. With different rotation speed each. How is this possible?
Thank you in advance!
Just to be clear:
When using SpriteBatch.Draw() with origin and angle, there is only one rotation: the final angle of the sprite.
The other rotations are positional offsets.
The origin in the Draw() call is a translation, rotation, translate back. Your transform matrix shows this quite well:
Matrix transform = Matrix.CreateTranslation(-origin.X, -origin.Y, 0f) *
Matrix.CreateRotationZ(rotation) *
Matrix.CreateTranslation(origin.X, origin.Y, 0f);
//Class level variables:
float ScreenRotation, ScreenRotationSpeed;
float ObjectRotation, ObjectRotationSpeed;
Vector2 ScreenOrigin, SpriteOrigin;
// ...
// In constructor and resize events:
ScreenOrigin = new Vector2(Basic.width <<1, Basic.height <<1);
// shifts are faster for `int` type. If "Basic.width" is `float`:
//ScreenOrigin = new Vector2(Basic.width, Basic.height) * 0.5f;
// In Update():
ScreenRotation += ScreenRotationSpeed; // * gameTime.ElapsedGameTime.Seconds; // for FPS invariant speed where speed = 60 * single frame speed
ObjectRotation+= ObjectRotationSpeed;
//Calculate the screen center rotation once per step
Matrix baseTransform = Matrix.CreateTranslation(-ScreenOrigin.X, -ScreenOrigin.Y, 0f) *
Matrix.CreateRotationZ(ScreenRotation) *
Matrix.CreateTranslation(ScreenOrigin.X, ScreenOrigin.Y, 0f);
// In Draw() at the start of your code snippet posted:
// moved outside of the loop for a translationally invariant vertical y interpretation
// or move it inside the loop and apply -y to position.Y for an elliptical effect
Vector2 ObjectOrigin = new Vector2(position.X, position.Y);
Matrix transform = baseTransform *
Matrix.CreateTranslation(-ObjectOrigin.X, -ObjectOrigin.Y, 0f) *
Matrix.CreateRotationZ(ObjectRotation) *
Matrix.CreateTranslation(ObjectOrigin.X, ObjectOrigin.Y, 0f);
foreach(var s in stacked)
{
Vector2 pos = new Vector2(ObjectOrigin.X, ObjectOrigin.Y - y);
pos = Vector2.Transform(pos, transform);
float DrawAngle = ObjectRotation;
// or float DrawAngle = ScreenRotation;
// or float DrawAngle = ScreenRotation + ObjectRotation;
// or float DrawAngle = 0;
s.Draw(pos, SpriteOrigin, DrawAngle, Color.White);
}
I suggest moving the Draw() parameter away from destinationRectangle and use the Vector2 position directly with scaling. Rotations within square rectangles can differ up to SQRT(2) in aspect ratio, i.e. stretching/squashing. Using Vector2 incurs a cost of higher collision complexity.
I am sorry for the ors, but without complete knowledge of the problem...YMMV
In my 2D projects, I use the vector form of polar coordinates.
The Matrix class requires more calculations than the polar equivalents in 2D. Matrix operates in 3D, wasting cycles calculating Z components.
With normalized direction vectors (cos t,sin t) and a radius(vector length),in many cases I use Vector2.LengthSquared() to avoid the square root when possible.
The only time I have used Matrices in 2D is display projection matrix(entire SpriteBatch) and Mouse and TouchScreen input deprojection(times the inverse of the projection matrix)

Having a point from 3 static cameras prespectives how to restore its position in 3d space?

We have same rectangle position relative to 3 same type of staticly installed web cameras that are not on the same line. Say on a flat basketball field. Thus we have tham all inside one 3d space and (x, y, z); (ax, ay, az); positionas and orientations set for all of them.
We have a ball color and we found its position on all 3 images im1, im2, im3. Now having its position on 2d frames (p1x, p1y);(p2x, p2y);(p3x, p3y), and cameras pos\orientations how to get ball position in 3d space?
You need to unproject 2D screen coordinates into 3D coordinates in space.
You need to solve system of equation to find real point in 3D from 3 rays you got on the first step.
You can find source code for gluUnProject here. I also provide here my code for it:
public Vector4 Unproject(float x, float y, Matrix4 View)
{
var ndcX = x / Viewport.Width * 2 - 1.0f;
var ndcY = y / Viewport.Height * 2 - 1.0f;
var invVP = Matrix4.Invert(View * ProjectionMatrix);
// We don't z-coordinate of the point, so we choose 0.0f for it.
// We are going to find out it later.
var screenPos = new Vector4(ndcX, -ndcY, 0.0f, 1.0f);
var res = Vector4.Transform(screenPos, invVP);
return res / res.W;
}
Vector3 ComputeRay(Camera camera, Vector2 p)
{
var worldPos = Unproject(p.X, p.Y, camera.View);
var dir = new Vector3(worldPos) - camera.Eye;
return new Ray(camera.Eye, Vector3.Normalize(dir));
}
Now you need to find intersection of three such rays. Theoretically that would be enough to use only two rays. It depends on positions of your cameras.
If we had infinite precision floating point arithmetic and input was without noise that would be trivial. But in reality you might need to exploit some simple numerical scheme to find the point with an appropriate precision.

How to convert world rotation to screen rotation?

I need to convert the position and rotation on a 3d object to screen position and rotation. I can convert the position easily but not the rotation. I've attempted to convert the rotation of the camera but it does not match up.
Attached is an example plunkr & conversion code.
The white facebook button should line up with the red plane.
https://plnkr.co/edit/0MOKrc1lc2Bqw1MMZnZV?p=preview
function toScreenPosition(position, camera, width, height) {
var p = new THREE.Vector3(position.x, position.y, position.z);
var vector = p.project(camera);
vector.x = (vector.x + 1) / 2 * width;
vector.y = -(vector.y - 1) / 2 * height;
return vector;
}
function updateScreenElements() {
var btn = document.querySelector('#btn-share')
var pos = plane.getWorldPosition();
var vec = toScreenPosition(pos, camera, canvas.width, canvas.height);
var translate = "translate3d("+vec.x+"px,"+vec.y+"px,"+vec.z+"px)";
var euler = camera.getWorldRotation();
var rotate = "rotateX("+euler.x+"rad)"+
" rotateY("+(euler.y)+"rad)"+
" rotateY("+(euler.z)+"rad)";
btn.style.transform= translate+ " "+rotate;
}
... And a screenshot of the issue.
I would highly recommend not trying to match this to the camera space, but instead to apply the image as a texture map to the red plane, and then use a raycast to see whether a click goes over the plane. You'll save yourself headache in translating and rotating and then hiding the symbol when it's behind the cube, etc
check out the THREEjs examples to see how to use the Raycaster. It's a lot more flexible and easier than trying to do rotations and matching. Then whatever the 'btn' onclick function is, you just call when you detect a raycast collision with the plane

Three.js - Drawing a torus but unable to understand the equation defined it

I try to do an animation which represents a sphere around which camera is rotating and I have drawn a circle on it (drawn with a THREE.TorusGeometry).
Then, I project a plane on the current point defined by the direction from camera position to the origin (0,0,0).
For a circle defined by y=0 and x²+z²=1 (i.e a circle defined into Oxz plane = equatorial plane of the sphere), you can see the result on :
link 1 : circle defined by y=0 and x²+z²=1
As you can see, the coordinates of plane are well drawn but I can't get to understand why the yellow circle is not drawn into Oxz plane (in this link, you can see that it is in Oxy plane).
Before the matrix multiplication, I defined above the vector of Torus by :
var coordTorus = new THREE.Vector3(radius*Math.cos(timer), 0, radius*Math.sin(timer));
i.e, by x'²+z'²=1 and y'=0 (choice 2). In this case, I don't get a valid result for the yellow circle, it is drawn into Oxy plane and not into Oxz plane like expected.
To get a good result, I have to define x'²+y'²=1 and z'=0 in local plane but I can't understand why ?
If someone could tell me the explication ?
It was hard to extract from all the code where exactly your problem was. I cleaned things up and solved it differently and I think this Fiddle shows what you wanted.
Instead of rotating all objects I rotated only the camera which seems much simpler then your solution:
/**
* Rotate camera
*/
function rotateCamera() {
// For camera rotation
stepSize += 0.002;
alpha = 2 * Math.PI * stepSize;
if (alpha > 2 * Math.PI) {
stepSize = 0;
}
// Rotate camera around a circle
camera.position.x = center.x + distance * Math.cos(alpha);
camera.position.z = center.y + distance * Math.sin(alpha);
// Camera should look at center
camera.lookAt(new THREE.Vector3(0, 0, 0));
}
And then I added your tangent plane to the camera instead of the scene:
So it rotates with the camera.
camera.add(plane);

Drawing lines between the Icosahedron vertices without wireframe material and with some line width using WEBGLRenderer

I'm new to threejs
I need to draw a sphere connected with triangles. I use Icosahedron to construct the sphere in the following way
var material = new THREE.MeshPhongMaterial({
emissive : 0xffffff,
transparent: true,
opacity : 0.5,
wireframe : true
});
var icogeo = new THREE.IcosahedronGeometry(80,2);
var mesh = new THREE.Mesh(icogeo, material);
scean.add(mesh);
But i need the width of the line to be more but line width won't show up in windows so i taught of looping through the vertices and draw a cylinder/tube between the vertices. (I can't draw lines because the LineBasicMaterial was not responding to Light.)
for(i=0;i<icogeo.faces.length;i++){
var face = icogeo.faces[i];
//get vertices from face and draw cylinder/tube between the three vertices
}
Can some one please help on drawing the tube/cylinder between two vector3 vertices?
**the problem i'm facing with wireframe was it was not smooth and i can't increase width of it in windows.
If you really want to create a cylinder between two points one way to do is to create it in a unit space and then transform it to your line. But that is very mathy.
An intuitive way to create it is to think about how would you do it in a unit space? A circle around the z axis (in x,y) and another one a bit down z.
Creating a circle in 2d is easy: for ( angle(0,360,360/numsteps) ) (x,y)=(sin(angle),cos(angle))*radius. (see for example Calculating the position of points in a circle).
Now the two butt ends of your cylinder are not in x,y! But If you have two vectors dx,dy you can just multiply your x,y with them and get a 3d position!
So how to get dx, dy? One way is http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
which reads way more scary than it is. You start with your forward direction, which is your line. forward = normalize(end-start). Then you just pick a direction "up". Usually (0,1,0). Unless forward is already close to up, then pick another one like (1,0,0). Take their cross product. This gives you "left". Then take the cross product between "left" and "forward" to get "right". Now "left" and "right" are you dx and dy!
That way you can make two circles at the two ends of your line. Add triangles in between and you have a cylinder!
Even though I do believe it is an overkill for what you are trying to achieve, here is code that draws a capsule (cylinder with spheres at the end) between two endpoints.
/**
* Returns a THREE.Object3D cylinder and spheres going from top to bottom positions
* #param radius - the radius of the capsule's cylinder
* #param top, bottom - THREE.Vector3, top and bottom positions of cone
* #param radiusSegments - tessellation around equator
* #param openTop, openBottom - whether the end is given a sphere; true means they are not
* #param material - THREE.Material
*/
function createCapsule (radius, top, bottom, radiusSegments, openTop, openBottom, material)
{
radiusSegments = (radiusSegments === undefined) ? 32 : radiusSegments;
openTop = (openTop === undefined) ? false : openTop;
openBottom = (openBottom === undefined) ? false : openBottom;
var capsule = new THREE.Object3D();
var cylinderAxis = new THREE.Vector3();
cylinderAxis.subVectors (top, bottom); // get cylinder height
var cylinderGeom = new THREE.CylinderGeometry (radius, radius, cylinderAxis.length(), radiusSegments, 1, true); // open-ended
var cylinderMesh = new THREE.Mesh (cylinderGeom, material);
// get cylinder center for translation
var center = new THREE.Vector3();
center.addVectors (top, bottom);
center.divideScalar (2.0);
// pass in the cylinder itself, its desired axis, and the place to move the center.
makeLengthAngleAxisTransform (cylinderMesh, cylinderAxis, center);
capsule.add (cylinderMesh);
if (! openTop || ! openBottom)
{
// instance geometry
var hemisphGeom = new THREE.SphereGeometry (radius, radiusSegments, radiusSegments/2, 0, 2*Math.PI, 0, Math.PI/2);
// make a cap instance of hemisphGeom around 'center', looking into some 'direction'
var makeHemiCapMesh = function (direction, center)
{
var cap = new THREE.Mesh (hemisphGeom, material);
makeLengthAngleAxisTransform (cap, direction, center);
return cap;
};
// ================================================================================
if (! openTop)
capsule.add (makeHemiCapMesh (cylinderAxis, top));
// reverse the axis so that the hemiCaps would look the other way
cylinderAxis.negate();
if (! openBottom)
capsule.add (makeHemiCapMesh (cylinderAxis, bottom));
}
return capsule;
}
// Transform object to align with given axis and then move to center
function makeLengthAngleAxisTransform (obj, align_axis, center)
{
obj.matrixAutoUpdate = false;
// From left to right using frames: translate, then rotate; TR.
// So translate is first.
obj.matrix.makeTranslation (center.x, center.y, center.z);
// take cross product of axis and up vector to get axis of rotation
var yAxis = new THREE.Vector3 (0, 1, 0);
// Needed later for dot product, just do it now;
var axis = new THREE.Vector3();
axis.copy (align_axis);
axis.normalize();
var rotationAxis = new THREE.Vector3();
rotationAxis.crossVectors (axis, yAxis);
if (rotationAxis.length() < 0.000001)
{
// Special case: if rotationAxis is just about zero, set to X axis,
// so that the angle can be given as 0 or PI. This works ONLY
// because we know one of the two axes is +Y.
rotationAxis.set (1, 0, 0);
}
rotationAxis.normalize();
// take dot product of axis and up vector to get cosine of angle of rotation
var theta = -Math.acos (axis.dot (yAxis));
// obj.matrix.makeRotationAxis (rotationAxis, theta);
var rotMatrix = new THREE.Matrix4();
rotMatrix.makeRotationAxis (rotationAxis, theta);
obj.matrix.multiply (rotMatrix);
}

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