Develop Reference

Node drifts of after 3D rotation in JavaFx

I get the x- and y-orientation from an RFID-Tag and want to animate the movement in a JavaFX application. It's my first java project so I'm sorry if there are stupid mistakes.
I rotate an box-node in the way of this and this thread.
Two pictures of how the green node rotates in front of the RFID-reader image in the background
xAxis=red, yAxis=green, zAxis=blue
.
I call the rotateNode method like that:
// calculate necessary variables:
delta_x = -x_angle + x_angle_old;
delta_y = -y_angle + y_angle_old;
delta_x_radians = Math.toRadians(delta_x);
delta_y_radians = Math.toRadians(delta_y);
pitch_rad = delta_y_radians;
yaw_rad = 0d; // not used at the moment
roll_rad = delta_x_radians;
if (!((roll_rad == 0d) && (pitch_rad == 0d) && (yaw_rad == 0d))) {
rotateNode(model3D, pitch_rad, yaw_rad, roll_rad);
}
My box-node has the position (0,0,-200) at the beginning and the center of the object should stay in that position the hole time. Just the orientation in two directions should change. My rotateNode method looks like this:
public static void rotateNode(Group n, double pitch_rad, double yaw_rad, double roll_rad) {// , TranslateTransition
// tt_z) {
double A11 = Math.cos(roll_rad) * Math.cos(yaw_rad);
double A12 = Math.cos(pitch_rad) * Math.sin(roll_rad)
+ Math.cos(roll_rad) * Math.sin(pitch_rad) * Math.sin(yaw_rad);
double A13 = Math.sin(roll_rad) * Math.sin(pitch_rad)
- Math.cos(roll_rad) * Math.cos(pitch_rad) * Math.sin(yaw_rad);
double A21 = -Math.cos(yaw_rad) * Math.sin(roll_rad);
double A22 = Math.cos(roll_rad) * Math.cos(pitch_rad)
- Math.sin(roll_rad) * Math.sin(pitch_rad) * Math.sin(yaw_rad);
double A23 = Math.cos(roll_rad) * Math.sin(pitch_rad)
+ Math.cos(pitch_rad) * Math.sin(roll_rad) * Math.sin(yaw_rad);
double A31 = Math.sin(yaw_rad);
double A32 = -Math.cos(yaw_rad) * Math.sin(pitch_rad);
double A33 = Math.cos(pitch_rad) * Math.cos(yaw_rad);
double d = Math.acos((A11 + A22 + A33 - 1d) / 2d);
if (d != 0d) {
double den = 2d * Math.sin(d);
if (den != 0d) {
Point3D p = new Point3D((A32 - A23) / den, (A13 - A31) / den, (A21 - A12) / den);
x_pos_node = (n.localToScene(n.getBoundsInLocal()).getMaxX()
+ n.localToScene(n.getBoundsInLocal()).getMinX()) / 2d;
y_pos_node = (n.localToScene(n.getBoundsInLocal()).getMaxY()
+ n.localToScene(n.getBoundsInLocal()).getMinY()) / 2d;
z_pos_node = (n.localToScene(n.getBoundsInLocal()).getMaxZ()
+ n.localToScene(n.getBoundsInLocal()).getMinZ()) / 2d;
r.setPivotX(x_pos_node);
r.setPivotY(y_pos_node);
r.setPivotZ(z_pos_node);
r.setAxis(p);
r.setAngle(Math.toDegrees(d));
n.getTransforms().add(r);
Transform all = n.getLocalToSceneTransform();
n.getTransforms().clear();
n.getTransforms().add(all);
}
}
}
Printing the following variables shows that the node moves in y although I don't want that to happen. Also I see, that slowly with time the pivot point of the rotation isn't in the center of the node anymore and when I turn the RFID-Tag it doesn't spin around the middle of the node it spins in a circle which gets bigger and bigger..
from:
x_pos_node: 0,00
y_pos_node: 0,39
z_pos_node: -200,00
MaxX: 199,00
MinX: -199,00
MaxY: 2,78
MinY: -2,00
MaxZ: -176,12
MinZ: -223,88
Depth: 47,76
Height: 4,78
Width: 398,00
to:
x_pos_node: 0,00
y_pos_node: 15,52
z_pos_node: -200,00
MaxX: 198,51
MinX: -198,51
MaxY: 38,35
MinY: -7,31
MaxZ: -130,85
MinZ: -269,15
Depth: 138,30
Height: 45,67
Width: 397,02
Picture from the side that shows how the green node moves under blue z-Axis / zero line:
.
Where is my mistake? Why does the object slowly moves instead of just rotating?
It is possible to fix the wrong position when I add an Translation:
n.getTransforms().add(new Translate(0, -y_pos_node, 0));
But that's just an hotfix and you can see how the object moves down and up again.. I think there is an error in the calculations or the positioning of the pivot point. It also turns a bit around the green y-Axis although "yaw_rad" is set to 0;

Directional helix for game missiles

my math isnt too great but im trying to learn though..
What im trying to do is give my games missiles a helix rocket effect, but i dont know how to work the Sin and Cos to make the helix play out in the right direction..
This is a 3D game by the way:
The problem is, depending on which direction the missile faces, the helix looks warped or flat..
Whats the best way to mathematically calculate a helix based on the missiles X,Y,Z/direction?, ive been trying to figure it out for a long time :/
Thanks alot!
double x = radius * Math.cos(theta);
double y = radius * Math.sin(theta);
double z = radius * Math.cos(theta);
location.add(x,y,z);
missile.shootFlame(location,2);
location.subtract(x,y,z);

Basis vectors
you need the overall direction of missile as 3D vector let call it W. From it you need to get 2 another vectors U,V which are all perpendicular to each other. To get them you can exploit cross product. So:
make W unit vector
Just W = W/|W| so:
l=sqrt(Wx*Wx+Wy*Wy+Wz*Wz);
Wx/=l;
Wy/=l;
Wz/=l;
choose U as any direction non parallel to W
so start with U=(1.0,0.0,0.0) and if U==W choose U=(0.0,1.0,0.0). If you got anything to lock to use that as U direction so the coordinate system will not rotate with time (like Up,North,Sun ...)
U should be unit so if not normalize it just like in #1
compute V
It should be perpendicular to U,W so use cross product:
V = W x U
Cross product of unit vectors is also unit vector so no need to normalize.
recompute U
As we choose the U manually we need to make sure it is also perpendicular to V,W so:
U = V x W
Now we have 3 perpendicular basis vectors where U,V lies in plane of the helix screws and W is the overall movement direction.
If you do not know how to compute the cross product see:
Understanding 4x4 homogenous transform matrices look for [edit2].
Now the Helix is easy:
Defines
so we have U,V,W on top of that we need radius r [units], movement speed v [units/s], angular speed o [rad/s] time t>=0.0 [s] and start position P0.
Helix equation
What we need is equation returning actual position for time so:
ang = o*t;
P(t) = P0 + U*r*cos(ang) + V*r*sin(ang) + W*v*t;
rewritten to scalars:
ang = o*t;
x = P0x + Ux*r*cos(ang) + Vx*r*sin(ang) + Wx*v*t;
y = P0y + Uy*r*cos(ang) + Vy*r*sin(ang) + Wy*v*t;
z = P0z + Uz*r*cos(ang) + Vz*r*sin(ang) + Wz*v*t;
[edit1] as you are incompetent to copy paste and or changing my code correctly...
Vector w = loc.getDirection();
double wX = w.getX();
double wY = w.getY();
double wZ = w.getZ();
double l = Math.sqrt((wX * wX) + (wY * wY) + (wZ * wZ));
wX = wX / l;
wY = wY / l;
wZ = wZ / l;
w = new Vector(wX,wY,wZ); // you forget to change W and use it latter ...
Vector u = new Vector(0, 1.0, 0);
if (Math.abs(wX)<1e-3) // if U and W are the same chose different U
if (Math.abs(wZ)<1e-3)
u = new Vector(1.0, 0.0, 0);
Vector v = w.crossProduct(u);
u = v.crossProduct(w);
double radius = 10; // helix radius [units]
double speed = 2.00; // movement speed [unit/s]
double omega = 0.628; // angular speed [rad/s]
//double omega = 36.0; // angular speed [deg/s]
for (double i = 0; i < 100; i += 1.0) // time [s]
{
double angle = omega * i; // actual screw position [rad] or [deg]
double x = u.getX() * radius * Math.cos(angle) + v.getX() * radius * Math.sin(angle) + wX * speed * i;
double y = u.getY() * radius * Math.cos(angle) + v.getY() * radius * Math.sin(angle) + wY * speed * i;
double z = u.getZ() * radius * Math.cos(angle) + v.getZ() * radius * Math.sin(angle) + wZ * speed * i;
loc.add(x,y,z); // What is this? should not you set the x,y,z instead of adding?
//do work
loc.subtract(x,y,z); // what is this?
}
This should provide you with helix points with traveled linear distance
speed*imax = 2.0*100.0 = 200.0 units
And screws:
omega*imax/(2*Pi) ~= 0.628*100.0/6.28 ~= 10 screws // in case of sin,cos want [rad]
omega*imax/360.0 = 36.0*100.0/360 = 10.0 screws // in case of sin,cos want [deg]
Do not forget to rem in/out the correct omega line (I choose [rad] as that is what I am used that my math libs use). Not sure If I translated to your environment correctly there may be bugs like abs has different name or u = new Vector(1.0, 0.0, 0); can be done on intermediate or declaration of variable only etc which I do not know as I do not code in it.

Java: Rotations and 3D distortions

I'm writing a program that will rotate a rectangular prism around a point. It handles the rotations via 3 rotation methods that each manage a rotation around a single axis (X, Y, and Z). Here's the code
public void spinZ(Spin spin) {
if (x == 0 && y == 0) {
return;
}
double mag = Math.sqrt(x * x + y * y);
double pxr = Math.atan(y / x);
x = Math.cos(spin.zr + pxr) * mag;
y = Math.sin(spin.zr + pxr) * mag;
}
public void spinY(Spin spin) {
if (z == 0 && x == 0) {
return;
}
double mag = Math.sqrt(x * x + z * z);
double pxr = Math.atan(z / x);
x = Math.cos(spin.yr + pxr) * mag;
z = Math.sin(spin.yr + pxr) * mag;
}
public void spinX(Spin spin) {
if (z == 0 && y == 0) {
return;
}
double mag = Math.sqrt(y * y + z * z);
double pxr = Math.atan(z / y);
y = Math.cos(spin.xr + pxr) * mag;
z = Math.sin(spin.xr + pxr) * mag;
}
public void addSpin(Spin spin) {
spinY(spin);
spinX(spin);
spinZ(spin);
}
Spin is a useless class that stores three doubles (which are rotations). These methods basically convert the rotations into 2D vectors (how I store the points) and rotate them as such. The first if statement makes sure the 2D vectors don't a magnitude of 0. They are allowed to, but in that case it's not necessary to carry out the rotation calculations. The other part just handles the trig. The bottom method just ties everything together and allows me to quickly change the order of the rotations (because order should and does affect the final rotation).
The problem isn't with the individual rotations but when they all come together. I can easily get a single rotation around a single axis to work without distorting the rectangular prism. When I put them all together, like if you were to call addSpin().
When spinY is called first, the prism is distorted when the rotations include a Y rotation (if the y component of the rotation is zero, and no rotation around the y-axis should occur, then no distortion occurs). In fact, if spinY() is called anytime but last a distortion of the cube will occur.
The same is the case with spinZ(). If spinZ() is called last, the cube won't get warped. However spinX() can go anywhere and not cause a distortion.
So the question is: Is there a problem with how I'm going about the rotations? The other question is while all rotations cannot be encompassed by rotations along just the X and Y axes or any other pair of distinct axes (like X and Z, or Y and Z), can those three sets collectively make all rotations? To clarify, can the rotations, which cannot be reached by a set of rotations around the X and Y axes, be reached by a set of rotations around the X and Z axes or the Y and Z axes?
I trust the medium I'm using to display the prisms. It's a ray-tracer I made that works well with rectangular prisms. This is a more math-based question, but it has a fairly comprehensive programming component.
These are some parallel calculations that still yield in distortions.
public void spinZ(Spin spin) {
double c = Math.cos(spin.yr);
double s = Math.sin(spin.yr);
double xp = x*c - y*s;
double yp = y*s + x*c;
x = xp;
y = yp;
}
public void spinY(Spin spin) {
double c = Math.cos(spin.yr);
double s = Math.sin(spin.yr);
double zp = z*c - x*s;
double xp = z*s + x*c;
x = xp;
z = zp;
}
public void spinX(Spin spin) {
double c = Math.cos(spin.yr);
double s = Math.sin(spin.yr);
double yp = y*c - z*s;
double zp = z*c + y*s;
y = yp;
z = zp;
}

Your checks for things like
x == 0
are unnecessary and dangerous as a double almost never will have the precise value 0. The atan when you have a division can lead to catastrophic loss of precision as well.
Why are they unnecessary? Because the following performs your rotation in a cleaner (numerically stable) fashion:
double c = Math.cos(spin.yr);
double s = Math.cos(spin.yr);
double zp = z*c - x*s;
double xp = z*s + x*c;
x = xp;
z = zp;
Of course, my example assumes you treat the y rotation with a right handed orientation, but from your sample code you seem to be treating it as left handed. Anyways, the wikipedia article on the Rotation matrix explains the math.

java 2d net gravity calculation

I am trying to calculate the net acceleration due to gravity in order to build a simple space flight sim using (G*(m1 * m2) / d * d) / m1. The ship tends to go in a semi-correct direction in a stair step pattern.
The update function of the main class
public void update()
{
double[] accels = new double[bodies.size()];//acceleration of the planets
double[][] xyaccels = new double[bodies.size()][2];//storing the x and y
for(Body n: bodies){
int count = 0;
double dist = distance(ship.loc.x,ship.loc.y,n.loc.x,n.loc.y);
double acel = getAccel(n.mass, ship.mass, dist);
accels[count] = acel;
double alpha = getAngle(ship.loc.x,ship.loc.y,n.loc.x,n.loc.y);
//xyaccels[count][0] = Math.cos(alpha) * acel;
//xyaccels[count][1] = Math.sin(alpha) * acel;
//split the acceleration into the x and y
XA += Math.cos(alpha) * acel;
YA += Math.sin(alpha) * acel;
count++;
}
ship.update(XA, YA);
//XA = 0;
//YA = 0;
accels = null;
xyaccels = null;
}
update function for the spaceship
public void update(double XA, double YA){
xAccel += XA;
yAccel += YA;
//add the x-acceleration and the y-acceleration to the loc
loc.x += Math.round(xAccel);
loc.y += Math.round(yAccel);
}

You don't update location from acceleration. You don't have any equations relating velocity to acceleration that I can see. Your physics are wrong.
The 2D n body problem requires four coupled ordinary differential equations for each body. Acceleration, velocity, and displacement are all 2D vector quantities.
dv/dt = F/m // Newton's F = ma
ds/dt = v // Definition of velocity that you'll update to get position.
You have to integrate all of them together.
I'm assuming you know something about calculus and physics. If you don't, it's a better idea to find a library written by someone else who does: something like JBox2D.

Z-buffering algorithm not drawing 100% correctly

I'm programming a software renderer in Java, and am trying to use Z-buffering for the depth calculation of each pixel. However, it appears to work inconsistently. For example, with the Utah teapot example model, the handle will draw perhaps half depending on how I rotate it.
My z-buffer algorithm:
for(int i = 0; i < m_triangles.size(); i++)
{
if(triangleIsBackfacing(m_triangles.get(i))) continue; //Backface culling
for(int y = minY(m_triangles.get(i)); y < maxY(m_triangles.get(i)); y++)
{
if((y + getHeight()/2 < 0) || (y + getHeight()/2 >= getHeight())) continue; //getHeight/2 and getWidth/2 is for moving the model to the centre of the screen
for(int x = minX(m_triangles.get(i)); x < maxX(m_triangles.get(i)); x++)
{
if((x + getWidth()/2 < 0) || (x + getWidth()/2 >= getWidth())) continue;
rayOrigin = new Point2D(x, y);
if(pointWithinTriangle(m_triangles.get(i), rayOrigin))
{
zDepth = zValueOfPoint(m_triangles.get(i), rayOrigin);
if(zDepth > zbuffer[x + getWidth()/2][y + getHeight()/2])
{
zbuffer[x + getWidth()/2][y + getHeight()/2] = zDepth;
colour[x + getWidth()/2][y + getHeight()/2] = m_triangles.get(i).getColour();
g2.setColor(m_triangles.get(i).getColour());
drawDot(g2, rayOrigin);
}
}
}
}
}
Method for calculating the z value of a point, given a triangle and the ray origin:
private double zValueOfPoint(Triangle triangle, Point2D rayOrigin)
{
Vector3D surfaceNormal = getNormal(triangle);
double A = surfaceNormal.x;
double B = surfaceNormal.y;
double C = surfaceNormal.z;
double d = -(A * triangle.getV1().x + B * triangle.getV1().y + C * triangle.getV1().z);
double rayZ = -(A * rayOrigin.x + B * rayOrigin.y + d) / C;
return rayZ;
}
Method for calculating if the ray origin is within a projected triangle:
private boolean pointWithinTriangle(Triangle triangle, Point2D rayOrigin)
{
Vector2D v0 = new Vector2D(triangle.getV3().projectPoint(modelViewer), triangle.getV1().projectPoint(modelViewer));
Vector2D v1 = new Vector2D(triangle.getV2().projectPoint(modelViewer), triangle.getV1().projectPoint(modelViewer));
Vector2D v2 = new Vector2D(rayOrigin, triangle.getV1().projectPoint(modelViewer));
double d00 = v0.dotProduct(v0);
double d01 = v0.dotProduct(v1);
double d02 = v0.dotProduct(v2);
double d11 = v1.dotProduct(v1);
double d12 = v1.dotProduct(v2);
double invDenom = 1.0 / (d00 * d11 - d01 * d01);
double u = (d11 * d02 - d01 * d12) * invDenom;
double v = (d00 * d12 - d01 * d02) * invDenom;
// Check if point is in triangle
if((u >= 0) && (v >= 0) && ((u + v) <= 1))
{
return true;
}
return false;
}
Method for calculating surface normal of a triangle:
private Vector3D getNormal(Triangle triangle)
{
Vector3D v1 = new Vector3D(triangle.getV1(), triangle.getV2());
Vector3D v2 = new Vector3D(triangle.getV3(), triangle.getV2());
return v1.crossProduct(v2);
}
Example of the incorrectly drawn teapot:
What am I doing wrong? I feel like it must be some small thing. Given that the triangles draw at all, I doubt it's the pointWithinTriangle method. Backface culling also appears to work correctly, so I doubt it's that. The most likely culprit to me is the zValueOfPoint method, but I don't know enough to know what's wrong with it.

My zValueOfPoint method was not working correctly. I'm unsure why :( however, I changed to a slightly different method of calculating the value of a point in a plane, found here: http://forum.devmaster.net/t/interpolation-on-a-3d-triangle-using-normals/20610/5
To make the answer here complete, we have the equation of a plane:
A * x + B * y + C * z + D = 0
Where A, B, and C are the surface normal x/y/z values, and D is -(Ax0 + By0 + Cz0).
x0, y0, and z0 are taken from one of the vertices of the triangle. x, y, and z are the coordinates of the point where the ray intersects the plane. x and y are known values (rayOrigin.x, rayOrigin.y) but z is the depth which we need to calculate. From the above equation we derive:
z = -A / C * x - B / C * y - D
Then, copied from the above link, we do:
"Note that for every step in the x-direction, z increments by -A / C, and likewise it increments by -B / C for every step in the y-direction.
So these are the gradients we're looking for to perform linear interpolation. In the plane equation (A, B, C) is the normal vector of the plane.
It can easily be computed with a cross product.
Now that we have the gradients, let's call them dz/dx (which is -A / C) and dz/dy (which is -B / C), we can easily compute z everywhere on the triangle.
We know the z value in all three vertex positions.
Let's call the one of the first vertex z0, and it's position coordinates (x0, y0). Then a generic z value of a point (x, y) can be computed as:"
z = z0 + dz/dx * (x - x0) + dz/dy * (y - y0)
This found the Z value correctly and fixed my code. The new zValueOfPoint method is:
private double zValueOfPoint(Triangle triangle, Point2D rayOrigin)
{
Vector3D surfaceNormal = getNormal(triangle);
double A = surfaceNormal.x;
double B = surfaceNormal.y;
double C = surfaceNormal.z;
double dzdx = -A / C;
double dzdy = -B / C;
double rayZ = triangle.getV1().z * modelViewer.getModelScale() + dzdx * (rayOrigin.x - triangle.getV1().projectPoint(modelViewer).x) + dzdy * (rayOrigin.y - triangle.getV1().projectPoint(modelViewer).y);
return rayZ;
}
We can optimize this by only calculating most of it once, and then adding dz/dx to get the z value for the next pixel, or dz/dy for the pixel below (with the y-axis going down). This means that we cut down on calculations per polygon significantly.

this must be really slow
so much redundant computations per iteration/pixel just to iterate its coordinates. You should compute the 3 projected vertexes and iterate between them instead look here:
triangle/convex polygon rasterization
I dislike your zValueOfPoint function
can not find any use of x,y coordinates from the main loops in it so how it can compute the Z value correctly ?
Or it just computes the average Z value per whole triangle ? or am I missing something? (not a JAVA coder myself) in anyway it seems that this is your main problem.
if you Z-value is wrongly computed then Z-Buffer can not work properly. To test that look at the depth buffer as image after rendering if it is not shaded teapot but some incoherent or constant mess instead then it is clear ...
Z buffer implementation
That looks OK
[Hints]
You have too much times terms like x + getWidth()/2 why not compute them just once to some variable? I know modern compilers should do it anyway but the code would be also more readable and shorter... at least for me