In the process of developing my own zoom system besides the ones provided by the Three.js controls, I need to find the current distance from camera to the plane that contains the (0, 0, 0) origin point and is perpendicular on the camera direction (let's call that value opdistance), so I can use it to translate the camera along its direction according to a zoomfactor value and a -1 or 1 bias value given by the mouse wheel, like so:
camera.translateZ(opdistance * zoomfactor ** bias - opdistance);
In a 2D triangle's mathematical terms, that distance is the camera .distanceTo the (0, 0, 0) origin point multiplied by the cosine of the angle between the camera direction and the camera to origin direction vectors and that can be calculated like:
var cameradirection = new THREE.Vector3();
camera.getWorldDirection(cameradirection);
var distancedirection = new THREE.Vector3();
camera.getWorldPosition(distancedirection).negate();
var positionangle = cameradirection.angleTo(distancedirection);
var opdistance = camera.position.distanceTo(new THREE.Vector3(0, 0, 0)) * Math.cos(positionangle);
camera.translateZ(opdistance * zoomfactor ** bias - opdistance);
but I'm interested in a simpler way using Three.js' standard methods, which I'm sure it exists.
The reason for asking is that I initially used the camera.position.z value as the opdistance, but that only works if the camera is instantiated with the (0, 0, 0) point "in front" of it along the Z axis, and it's otherwise changing to other values, depending on the camera position and direction (for example, the opdistance becomes the camera.position.y if the camera is placed "above" the (0, 0, 0) point and looking at it, and so on).
P.S. I could also achieve this via camera.position.setLength(finaldistance) but that produces some unwanted side effects as the camera jumps to other positions on resuming actions via other controls (probably some missing matrix update issue), so alternative ideas are welcomed.
In ThreeJS, if the camera is rotated at any given angle, how can I determine the coordinate of the point exactly 1 unit in the direction that the camera is facing.
If you are unfamiliar with ThreeJS camera rotation angles, the rotations are very very weird.
For example, if all of my rotation variable are 0, then the function would return (0, 0, -1).
If the rotation x is Pi / 2 (90 degrees), then the function would return (1, 0, 0)
How could I create a function to do this? I don't need everything, primarily just the math.
You want to get the world position of a point that is one unit in front of the camera.
One way to do that is to add an object in front of, and as a child of, the camera. Then you just need to query the world position of the object.
By default, when a camera's rotation is ( 0, 0, 0 ), the camera is looking down its negative z-axis. So here is the pattern to follow:
var object = new THREE.Object3D();
object.position.set( 0, 0, - 1 );
scene.add( camera ); // this is required when the camera has children
camera.add( object );
Now, you can get the point you need like so:
var worldPos = new THREE.Vector3(); // create once and reuse it
...
camera.updateMatrixWorld(); // this is called in the render loop, so you may not have to call it again. Experiment.
worldPos.setFromMatrixPosition( object.matrixWorld );
three.js r.71
There is an online 3d editor where you can edit individual meshes (move, scale, rotate). Ability to edit meshes implemented using custom transform controls which based on threejs's TransformControls code. This is fragment from mousemove event:
var intersect = intersectObjects(pointer, [xzPlane]); // intersect mouse's pointer with horizontal plane
var point = new THREE.Vector3();
point.copy(intersect.point);
point.sub(offset); // coords from mousedown event (from start stretching)
// some code for 'scale' value calculating base on 'point' variable
// var scale = ...;
//
mesh.scale.x = scale;
This code works well if the mesh does not rotate.
Requires scaling always happened to the world coordinate system. This is programming question
For example, from this:
To this:
P.S. I think that custom mesh matrix must be created, but I have very little experience with matrices
Thanks!
Instead of setting the rotation, like so:
mesh.rotation.set( Math.PI/4, 0, 0 );
apply the identical rotation to the geometry, instead:
var euler = new THREE.Euler( Math.PI / 4, 0, 0 );
mesh.geometry.applyMatrix( new THREE.Matrix4().makeRotationFromEuler( euler ) );
Now, you can set the scale and get the result you want.
mesh.scale.z = 2;
fiddle: http://jsfiddle.net/Tm7Ab/5/
three.js r.67
I have a camera that moves in a few different ways in the scene. The camera should rotate around a target position. In my case, this is a point on a mesh that the user has targeted. Because the camera usually doesn't require moving relative to this point, I was not able to use the pivot idea here: https://github.com/mrdoob/three.js/issues/1830. My current solution uses the following code:
var rotationY = new THREE.Matrix4();
var rotationX = new THREE.Matrix4();
var translation = new THREE.Matrix4();
var translationInverse = new THREE.Matrix4();
var matrix = new THREE.Matrix4();
function rotateCameraAroundObject(dx, dy, target) {
// collect up and right vectors from camera perspective
camComponents.up = rotateVectorForObject(new THREE.Vector3(0,1,0), camera.matrixWorld);
camComponents.right = rotateVectorForObject(new THREE.Vector3(1,0,0), camera.matrixWorld);
matrix.identity();
rotationX.makeRotationAxis(camComponents.right, -dx);
rotationY.makeRotationAxis(camComponents.up, -dy);
translation.makeTranslation(
target.position.x - camera.position.x,
target.position.y - camera.position.y,
target.position.z - camera.position.z);
translationInverse.getInverse(translation);
matrix.multiply(translation).multiply(rotationY).multiply(rotationX).multiply(translationInverse);
camera.applyMatrix(matrix);
camera.lookAt(target.position);
}
The issue is that we do not want to use lookAt, because of the reorientation. We want to be able to remove that line.
If we use the code above without lookAt, we rotate around the point but we do not look at the point. My understanding is that my method should rotate the camera's view as much as the camera itself is rotate, but instead the camera is rotated only a small amount. Could anyone help me understand what's wrong?
EDIT: Cleaned up the original post and code to hopefully clarify my question.
My thinking is that I can translate to the origin (my target position), rotate my desired amount, and then translate back to the beginning position. Because of the rotation, I expect to be in a new position looking at the origin.
In fact, I'm testing it now without the translation matrices being used, so the matrix multiplication line is:
matrix.multiply(rotationY).multiply(rotationX);
and it seems to be behaving the same. Thanks for all the help so far!
ONE MORE THING! A part of the problem is that when the camera behaves badly close to the north or south poles. I am looking for a 'free roaming' sort of feel.
Put the following in your render loop:
camera.position.x = target.position.x + radius * Math.cos( constant * elapsedTime );
camera.position.z = target.position.z + radius * Math.sin( constant * elapsedTime );
camera.lookAt( target.position );
renderer.render( scene, camera );
Alternatively, you can use THREE.OrbitControls or THREE.TrackballControls. See the three.js examples.
The Gimbal lock that you are referring to (reorientation) is because of the use of Euler angles in the default implementation of the camera lookat. If you set
camera.useQuaternion = true;
before your call to lookat, then euler angles will not be used. Would this solve your problem ?
I have been trying to work with the Projector and Ray classes in order to do some collision detection demos. I have started just trying to use the mouse to select objects or to drag them. I have looked at examples that use the objects, but none of them seem to have comments explaining what exactly some of the methods of Projector and Ray are doing. I have a couple questions that I am hoping will be easy for someone to answer.
What exactly is happening and what is the difference between Projector.projectVector() and Projector.unprojectVector()? I notice that it seems in all the examples using both projector and ray objects the unproject method is called before the ray is created. When would you use projectVector?
I am using the following code in this demo to spin the cube when dragged on with the mouse. Can someone explain in simple terms what exactly is happening when I unproject with the mouse3D and camera and then create the Ray. Does the ray depend on the call to unprojectVector()
/** Event fired when the mouse button is pressed down */
function onDocumentMouseDown(event) {
event.preventDefault();
mouseDown = true;
mouse3D.x = mouse2D.x = mouseDown2D.x = (event.clientX / window.innerWidth) * 2 - 1;
mouse3D.y = mouse2D.y = mouseDown2D.y = -(event.clientY / window.innerHeight) * 2 + 1;
mouse3D.z = 0.5;
/** Project from camera through the mouse and create a ray */
projector.unprojectVector(mouse3D, camera);
var ray = new THREE.Ray(camera.position, mouse3D.subSelf(camera.position).normalize());
var intersects = ray.intersectObject(crateMesh); // store intersecting objects
if (intersects.length > 0) {
SELECTED = intersects[0].object;
var intersects = ray.intersectObject(plane);
}
}
/** This event handler is only fired after the mouse down event and
before the mouse up event and only when the mouse moves */
function onDocumentMouseMove(event) {
event.preventDefault();
mouse3D.x = mouse2D.x = (event.clientX / window.innerWidth) * 2 - 1;
mouse3D.y = mouse2D.y = -(event.clientY / window.innerHeight) * 2 + 1;
mouse3D.z = 0.5;
projector.unprojectVector(mouse3D, camera);
var ray = new THREE.Ray(camera.position, mouse3D.subSelf(camera.position).normalize());
if (SELECTED) {
var intersects = ray.intersectObject(plane);
dragVector.sub(mouse2D, mouseDown2D);
return;
}
var intersects = ray.intersectObject(crateMesh);
if (intersects.length > 0) {
if (INTERSECTED != intersects[0].object) {
INTERSECTED = intersects[0].object;
}
}
else {
INTERSECTED = null;
}
}
/** Removes event listeners when the mouse button is let go */
function onDocumentMouseUp(event) {
event.preventDefault();
/** Update mouse position */
mouse3D.x = mouse2D.x = (event.clientX / window.innerWidth) * 2 - 1;
mouse3D.y = mouse2D.y = -(event.clientY / window.innerHeight) * 2 + 1;
mouse3D.z = 0.5;
if (INTERSECTED) {
SELECTED = null;
}
mouseDown = false;
dragVector.set(0, 0);
}
/** Removes event listeners if the mouse runs off the renderer */
function onDocumentMouseOut(event) {
event.preventDefault();
if (INTERSECTED) {
plane.position.copy(INTERSECTED.position);
SELECTED = null;
}
mouseDown = false;
dragVector.set(0, 0);
}
I found that I needed to go a bit deeper under the surface to work outside of the scope of the sample code (such as having a canvas that does not fill the screen or having additional effects). I wrote a blog post about it here. This is a shortened version, but should cover pretty much everything I found.
How to do it
The following code (similar to that already provided by #mrdoob) will change the color of a cube when clicked:
var mouse3D = new THREE.Vector3( ( event.clientX / window.innerWidth ) * 2 - 1, //x
-( event.clientY / window.innerHeight ) * 2 + 1, //y
0.5 ); //z
projector.unprojectVector( mouse3D, camera );
mouse3D.sub( camera.position );
mouse3D.normalize();
var raycaster = new THREE.Raycaster( camera.position, mouse3D );
var intersects = raycaster.intersectObjects( objects );
// Change color if hit block
if ( intersects.length > 0 ) {
intersects[ 0 ].object.material.color.setHex( Math.random() * 0xffffff );
}
With the more recent three.js releases (around r55 and later), you can use pickingRay which simplifies things even further so that this becomes:
var mouse3D = new THREE.Vector3( ( event.clientX / window.innerWidth ) * 2 - 1, //x
-( event.clientY / window.innerHeight ) * 2 + 1, //y
0.5 ); //z
var raycaster = projector.pickingRay( mouse3D.clone(), camera );
var intersects = raycaster.intersectObjects( objects );
// Change color if hit block
if ( intersects.length > 0 ) {
intersects[ 0 ].object.material.color.setHex( Math.random() * 0xffffff );
}
Let's stick with the old approach as it gives more insight into what is happening under the hood. You can see this working here, simply click on the cube to change its colour.
What's happening?
var mouse3D = new THREE.Vector3( ( event.clientX / window.innerWidth ) * 2 - 1, //x
-( event.clientY / window.innerHeight ) * 2 + 1, //y
0.5 ); //z
event.clientX is the x coordinate of the click position. Dividing by window.innerWidth gives the position of the click in proportion of the full window width. Basically, this is translating from screen coordinates that start at (0,0) at the top left through to (window.innerWidth,window.innerHeight) at the bottom right, to the cartesian coordinates with center (0,0) and ranging from (-1,-1) to (1,1) as shown below:
Note that z has a value of 0.5. I won't go into too much detail about the z value at this point except to say that this is the depth of the point away from the camera that we are projecting into 3D space along the z axis. More on this later.
Next:
projector.unprojectVector( mouse3D, camera );
If you look at the three.js code you will see that this is really an inversion of the projection matrix from the 3D world to the camera. Bear in mind that in order to get from 3D world coordinates to a projection on the screen, the 3D world needs to be projected onto the 2D surface of the camera (which is what you see on your screen). We are basically doing the inverse.
Note that mouse3D will now contain this unprojected value. This is the position of a point in 3D space along the ray/trajectory that we are interested in. The exact point depends on the z value (we will see this later).
At this point, it may be useful to have a look at the following image:
The point that we have just calculated (mouse3D) is shown by the green dot. Note that the size of the dots are purely illustrative, they have no bearing on the size of the camera or mouse3D point. We are more interested in the coordinates at the center of the dots.
Now, we don't just want a single point in 3D space, but instead we want a ray/trajectory (shown by the black dots) so that we can determine whether an object is positioned along this ray/trajectory. Note that the points shown along the ray are just arbitrary points, the ray is a direction from the camera, not a set of points.
Fortunately, because we a have a point along the ray and we know that the trajectory must pass from the camera to this point, we can determine the direction of the ray. Therefore, the next step is to subtract the camera position from the mouse3D position, this will give a directional vector rather than just a single point:
mouse3D.sub( camera.position );
mouse3D.normalize();
We now have a direction from the camera to this point in 3D space (mouse3D now contains this direction). This is then turned into a unit vector by normalizing it.
The next step is to create a ray (Raycaster) starting from the camera position and using the direction (mouse3D) to cast the ray:
var raycaster = new THREE.Raycaster( camera.position, mouse3D );
The rest of the code determines whether the objects in 3D space are intersected by the ray or not. Happily it is all taken care of us behind the scenes using intersectsObjects.
The Demo
OK, so let's look at a demo from my site here that shows these rays being cast in 3D space. When you click anywhere, the camera rotates around the object to show you how the ray is cast. Note that when the camera returns to its original position, you only see a single dot. This is because all the other dots are along the line of the projection and therefore blocked from view by the front dot. This is similar to when you look down the line of an arrow pointing directly away from you - all that you see is the base. Of course, the same applies when looking down the line of an arrow that is travelling directly towards you (you only see the head), which is generally a bad situation to be in.
The z coordinate
Let's take another look at that z coordinate. Refer to this demo as you read through this section and experiment with different values for z.
OK, lets take another look at this function:
var mouse3D = new THREE.Vector3( ( event.clientX / window.innerWidth ) * 2 - 1, //x
-( event.clientY / window.innerHeight ) * 2 + 1, //y
0.5 ); //z
We chose 0.5 as the value. I mentioned earlier that the z coordinate dictates the depth of the projection into 3D. So, let's have a look at different values for z to see what effect it has. To do this, I have placed a blue dot where the camera is, and a line of green dots from the camera to the unprojected position. Then, after the intersections have been calculated, I move the camera back and to the side to show the ray. Best seen with a few examples.
First, a z value of 0.5:
Note the green line of dots from the camera (blue dot) to the unprojected value (the coordinate in 3D space). This is like the barrel of a gun, pointing in the direction that they ray should be cast. The green line essentially represents the direction that is calculated before being normalised.
OK, let's try a value of 0.9:
As you can see, the green line has now extended further into 3D space. 0.99 extends even further.
I do not know if there is any importance as to how big the value of z is. It seems that a bigger value would be more precise (like a longer gun barrel), but since we are calculating the direction, even a short distance should be pretty accurate. The examples that I have seen use 0.5, so that is what I will stick with unless told otherwise.
Projection when the canvas is not full screen
Now that we know a bit more about what is going on, we can figure out what the values should be when the canvas does not fill the window and is positioned on the page. Say, for example, that:
the div containing the three.js canvas is offsetX from the left and offsetY from the top of the screen.
the canvas has a width equal to viewWidth and height equal to viewHeight.
The code would then be:
var mouse3D = new THREE.Vector3( ( event.clientX - offsetX ) / viewWidth * 2 - 1,
-( event.clientY - offsetY ) / viewHeight * 2 + 1,
0.5 );
Basically, what we are doing is calculating the position of the mouse click relative to the canvas (for x: event.clientX - offsetX). Then we determine proportionally where the click occurred (for x: /viewWidth) similar to when the canvas filled the window.
That's it, hopefully it helps.
Basically, you need to project from the 3D world space and the 2D screen space.
Renderers use projectVector for translating 3D points to the 2D screen. unprojectVector is basically for doing the inverse, unprojecting 2D points into the 3D world. For both methods you pass the camera you're viewing the scene through.
So, in this code you're creating a normalised vector in 2D space. To be honest, I was never too sure about the z = 0.5 logic.
mouse3D.x = (event.clientX / window.innerWidth) * 2 - 1;
mouse3D.y = -(event.clientY / window.innerHeight) * 2 + 1;
mouse3D.z = 0.5;
Then, this code uses the camera projection matrix to transform it to our 3D world space.
projector.unprojectVector(mouse3D, camera);
With the mouse3D point converted into the 3D space, we can now use it for getting the direction and then use the camera position to throw a ray from.
var ray = new THREE.Ray(camera.position, mouse3D.subSelf(camera.position).normalize());
var intersects = ray.intersectObject(plane);
As of release r70, Projector.unprojectVector and Projector.pickingRay are deprecated. Instead, we have raycaster.setFromCamera which makes the life easier in finding the objects under the mouse pointer.
var mouse = new THREE.Vector2();
mouse.x = (event.clientX / window.innerWidth) * 2 - 1;
mouse.y = -(event.clientY / window.innerHeight) * 2 + 1;
var raycaster = new THREE.Raycaster();
raycaster.setFromCamera(mouse, camera);
var intersects = raycaster.intersectObjects(scene.children);
intersects[0].object gives the object under the mouse pointer and intersects[0].point gives the point on the object where the mouse pointer was clicked.
Projector.unprojectVector() treats the vec3 as a position. During the process the vector gets translated, hence we use .sub(camera.position) on it. Plus we need to normalize it after after this operation.
I will add some graphics to this post but for now I can describe the geometry of the operation.
We can think of the camera as a pyramid in terms of geometry. We in fact define it with 6 panes - left, right, top, bottom, near and far (near being the plane closest to the tip).
If we were standing in some 3d and observing these operations, we would see this pyramid in an arbitrary position with an arbitrary rotation in space. Lets say that this pyramid's origin is at it's tip, and it's negative z axis runs towards the bottom.
Whatever ends up being contained within those 6 planes will end up being rendered on our screen if we apply the correct sequence of matrix transformations. Which i opengl go something like this:
NDC_or_homogenous_coordinates = projectionMatrix * viewMatrix * modelMatrix * position.xyzw;
This takes our mesh from it's object space into world space, into camera space and finally it projects it does the perspective projection matrix which essentially puts everything into a small cube (NDC with ranges from -1 to 1).
Object space can be a neat set of xyz coordinates in which you generate something procedurally or say, a 3d model, that an artist modeled using symmetry and thus neatly sits aligned with the coordinate space, as opposed to an architectural model obtained from say something like REVIT or AutoCAD.
An objectMatrix could happen in between the model matrix and the view matrix, but this is usually taken care of ahead of time. Say, flipping y and z, or bringing a model thats far away from the origin into bounds, converting units etc.
If we think of our flat 2d screen as if it had depth, it could be described the same way as the NDC cube, albeit, slightly distorted. This is why we supply the aspect ratio to the camera. If we imagine a square the size of our screen height, the remainder is the aspect ratio that we need to scale our x coordinates.
Now back to 3d space.
We're standing in a 3d scene and we see the pyramid. If we cut everything around the pyramid, and then take the pyramid along with the part of the scene contained in it and put it's tip at 0,0,0, and point the bottom towards the -z axis we will end up here:
viewMatrix * modelMatrix * position.xyzw
Multiplying this by the projection matrix will be the same as if we took the tip, and started pulling it appart in the x and y axis creating a square out of that one point, and turning the pyramid into a box.
In this process the box gets scaled to -1 and 1 and we get our perspective projection and we end up here:
projectionMatrix * viewMatrix * modelMatrix * position.xyzw;
In this space, we have control over a 2 dimensional mouse event. Since it's on our screen, we know that it's two dimensional, and that it's somewhere within the NDC cube. If it's two dimensional, we can say that we know X and Y but not the Z, hence the need for ray casting.
So when we cast a ray, we are basically sending a line through the cube, perpendicular to one of it's sides.
Now we need to figure out if that ray hits something in the scene, and in order to do that we need to transform the ray from this cube, into some space suitable for computation. We want the ray in world space.
Ray is an infinite line in space. It's different from a vector because it has a direction, and it must pass through a point in space. And indeed this is how the Raycaster takes its arguments.
So if we squeeze the top of the box along with the line, back into the pyramid, the line will originate from the tip and run down and intersect the bottom of the pyramid somewhere between -- mouse.x * farRange and -mouse.y * farRange.
(-1 and 1 at first, but view space is in world scale, just rotated and moved)
Since this is the default location of the camera so to speak (it's object space) if we apply it's own world matrix to the ray, we will transform it along with the camera.
Since the ray passes through 0,0,0, we only have it's direction and THREE.Vector3 has a method for transforming a direction:
THREE.Vector3.transformDirection()
It also normalizes the vector in the process.
The Z coordinate in the method above
This essentially works with any value, and acts the same because of the way the NDC cube works.
The near plane and far plane are projected onto -1 and 1.
So when you say, shoot a ray at:
[ mouse.x | mouse.y | someZpositive ]
you send a line, through a point (mouse.x, mouse.y, 1) in the direction of (0,0,someZpositive)
If you relate this to the box/pyramid example, this point is at the bottom, and since the line originates from the camera it goes through that point as well.
BUT, in the NDC space, this point is stretched to infinity, and this line ends up being parallel with the left,top,right,bottom planes.
Unprojecting with the above method turns this into a position/point essentially. The far plane just gets mapped into world space, so our point sits somewhere at z=-1, between -camera aspect and + cameraAspect on X and -1 and 1 on y.
since it's a point, applying the cameras world matrix will not only rotate it but translate it as well. Hence the need to bring this back to the origin by subtracting the cameras position.