I've been trying for the past few days to make a working implementation of a virtual trackball for the user interface for a 3D graphing-like program. But I'm having trouble.
Looking at the numbers and many tests the problems seems to be the actual concatenation of my quaternions but I don't know or think so. I've never worked with quaternions or virtual trackballs before, this is all new to me. I'm using the Quaternion class supplied by JOGL. I tried making my own and it worked (or at least as far a I know) but it was a complete mess so I just went with JOGL's.
When I do not concatenate the quaternions the slight rotations I see seem to be what I want, but of course It's hard when it's only moving a little bit in any direction. This code is based off of the Trackball Tutorial on the OpenGL wiki.
When I use the Quaternion class's mult (Quaternion q) method the graph hardly moves (even less than not trying to concatenate the quaternions).
When I tried Quaternionclass'sadd (Quaternion q)` method for the fun of it I get something that at the very least rotates the graph but not in any coherent way. It spazzes out and rotates randomly as I move the mouse. Occasionally I'll get quaternions entirely filled with NaN.
In my code I will not show either of these, I'm lost with what to do with my quaternions. I know I want to multiply them because as far as I'm aware that's how they are concatenated. But like I said I've had no success, I'm assuming the screw up is somewhere else in my code.
Anyway, my setup has a Trackball class with a public Point3f projectMouse (int x, int y) method and a public void rotateFor (Point3f p1, Point3f p2), Where Point3f is a class I made. Another class called Camera has a public void transform (GLAutoDrawable g) method which will call OpenGL methods to rotate based on the trackball's quaternion.
Here's the code:
public Point3f projectMouse (int x, int y)
{
int off = Screen.WIDTH / 2; // Half the width of the GLCanvas
x = x - objx_ - off; // obj being the 2D center of the graph
y = off - objy_ - y;
float t = Util.sq(x) + Util.sq(y); // Util is a class I made with
float rsq = Util.sq(off); // simple some math stuff
// off is also the radius of the sphere
float z;
if (t >= rsq)
z = (rsq / 2.0F) / Util.sqrt(t);
else
z = Util.sqrt(rsq - t);
Point3f result = new Point3f (x, y, z);
return result;
}
Here's the rotation method:
public void rotateFor (Point3f p1, Point3f p2)
{
// Vector3f is a class I made, I already know it works
// all methods in Vector3f modify the object's numbers
// and return the new modify instance of itself
Vector3f v1 = new Vector3f(p1.x, p1.y, p1.z).normalize();
Vector3f v2 = new Vector3f(p2.x, p2.y, p2.z).normalize();
Vector3f n = v1.copy().cross(v2);
float theta = (float) Math.acos(v1.dot(v2));
float real = (float) Math.cos(theta / 2.0F);
n.multiply((float) Math.sin(theta / 2.0F));
Quaternion q = new Quaternion(real, n.x, n.y, n.z);
rotation = q; // A member that can be accessed by a getter
// Do magic on the quaternion
}
EDIT:
I'm getting closer, I found out a few simple mistakes.
1: The JOGL implementation treats W as the real number, not X, I was using X for real
2: I was not starting with the quaternion 1 + 0i + 0j + 0k
3: I was not converting the quaternion into an axis/angle for opengl
4: I was not converting the angle into degrees for opengl
Also as Markus pointed out I was not normalizing the normal, when I did I couldn't see much change, thought it's hard to tell, he's right though.
The problem now is when I do the whole thing the graph shakes with a fierceness like you would never believe. It (kinda) moves in the direction you want it to, but the seizures are too fierce to make anything out of it.
Here's my new code with a few name changes:
public void rotate (Vector3f v1, Vector3f v2)
{
Vector3f v1p = v1.copy().normalize();
Vector3f v2p = v2.copy().normalize();
Vector3f n = v1p.copy().cross(v2p);
if (n.length() == 0) return; // Sometimes v1p equals v2p
float w = (float) Math.acos(v1p.dot(v2p));
n.normalize().multiply((float) Math.sin(w / 2.0F));
w = (float) Math.cos(w / 2.0F);
Quaternion q = new Quaternion(n.x, n.y, n.z, w);
q.mult(rot);
rot_ = q;
}
Here's the OpenGL code:
Vector3f p1 = tb_.project(x1, y1); // projectMouse [changed name]
Vector3f p2 = tb_.project(x2, y2);
tb_.rotate (p1, p2);
float[] q = tb_.getRotation().toAxis(); // Converts to angle/axis
gl.glRotatef((float)Math.toDegrees(q[0]), q[1], q[2], q[3]);
The reason for the name changes is because I deleted everything in the Trackball class and started over. Probably not the greatest idea, but oh well.
EDIT2:
I can say with pretty good certainty that there is nothing wrong with projecting onto the sphere.
I can also say that as far as the whole thing goes it seems to be the VECTOR that is the problem. The angle looks just fine, but the vector seems to jump around.
EDIT3:
The problem is the multiplication of the two quaternions, I can confirm that everything else works as expected. Something goes whacky with the axis during multiplication!
The problem is the multiplication of the two quaternions, I can confirm that everything else works as expected. Something goes whacky with the axis during multiplication!
You are absolutely correct!! I just recently submitted a correct multiplication and Jogamp has accepted my change. They had incorrect multiplication on mult(quaternion).
I am sure if you get the latest jogl release, it'll have the correct mult(Quaternion)
I did it!
Thanks to this C++ implementation I was able to develop a working trackball/arcball interface. My goodness me, I'm still not certain what the problem was, but I rewrote everything and even wrote my own Quaternions class and suddenly the whole thing works. I also made a Vectors class for vectors. I had a Vector3f class before but the Quaternions and Vectors classes are full of static methods and take in arrays. To make it easy to do vector computations on quaternions and vice versa. I will link the code for those two classes below, but only the Trackball class will be show here.
I made those two classes pretty quickly this morning so if there are any mathematical errors, well, uh, oops. I only used what I needed to use and made sure they were correct. These classes are below:
Quaternions: http://pastebin.com/raxS4Ma9
Vectors: http://pastebin.com/fU3PKZB9
Here is my Trackball class:
public class Trackball
{
private static final float RADIUS_ = Screen.DFLT_WIDTH / 2.0F;
private static final int REFRESH_ = 50;
private static final float SQRT2_ = (float) Math.sqrt(2);
private static final float SQRT2_INVERSE_ = 1.0F / SQRT2_;
private int count_;
private int objx_, objy_;
private float[] v1_, v2_;
private float[] rot_;
public Trackball ()
{
v1_ = new float[4];
v2_ = new float[4];
rot_ = new float[] {0, 0, 0, 1};
}
public void click (int x, int y)
{
v1_ = project(x, y);
}
public void drag (int x, int y)
{
v2_ = project(x, y);
if (Arrays.equals(v1_, v2_)) return;
float[] n = Vectors.cross(v2_, v1_, null);
float[] o = Vectors.sub(v1_, v2_, null);
float dt = Vectors.len(o) / (2.0F * RADIUS_);
dt = dt > 1.0F ? 1.0F : dt < -1.0F ? -1.0F : dt;
float a = 2.0F * (float) Math.asin(dt);
Vectors.norm_r(n);
Vectors.mul_r(n, (float) Math.sin(a / 2.0F));
if (count_++ == REFRESH_) { count_ = 0; Quaternions.norm_r(rot_); }
float[] q = Arrays.copyOf(n, 4);
q[3] = (float) Math.cos(a / 2.0F);
rot_ = Quaternions.mul(q, rot_, rot_);
}
public float[] getAxis ()
{
return Quaternions.axis(rot_, null);
}
public float[] project (float x, float y)
{
x = RADIUS_ - objx_ - x;
y = y - objy_ - RADIUS_;
float[] v = new float[] {x, y, 0, 0};
float len = Vectors.len(v);
float tr = RADIUS_ * SQRT2_INVERSE_;
if (len < tr)
v[2] = (float) Math.sqrt(RADIUS_ * RADIUS_ - len * len);
else
v[2] = tr * tr / len;
return v;
}
}
You can see there's a lot of similarities from the C++ example. Also I'd like to note there is no method for setting the objx_ and objy_ values yet. Those are for setting the center of the graph which can be moved around. Just saying, so you don't scratch your head about those fields.
The cross-product of two normalized vectors is not normalized itself. It's length is sin(theta). Try this instead:
n = n.normalize().multiply((float) Math.sin(theta / 2.0F));
Related
I am using LibGDX to make an orbit simulator (elliptical as planets possess their own initial velocity) and I have the physics mapped out like so:
public void move(float deltaTime, Planet planet) {
float deltaX = planet.getPos().x - this.pos.x;
float deltaY = planet.getPos().y - this.pos.y;
float alpha = (float) Math.toDegrees(Math.atan2(deltaY, deltaX));
float distance = (float) Math.sqrt(Math.pow(deltaX, 2) + Math.pow(deltaY, 2));
float F = G * this.m * planet.getM() / distance*distance;
this.force.x = F * MathUtils.cos(alpha);
this.force.y = F * MathUtils.sin(alpha);
this.vel.x += (this.force.x / this.m) * deltaTime;
this.vel.y += (this.force.y / this.m) * deltaTime;
this.pos.x += this.vel.x * deltaTime;
this.pos.y += this.vel.y * deltaTime;
}
The problem is that my planet wobbles around and doesn't orbit at all. I fear my calculations in the code might be wrong as the physics are definitely double-checked and correct.
Each celestial object is a planet and I have no 'Sun' classes of any type so far. Only one Planet class, which only has Getter and Setter methods, a render() method (which seems irrelevant) and the presented move() method.
I find nothing necessitates the following however I will add the parameters' values I chose for the both planets:
planet1 = new Planet(30, 1, new Vector2(300, 300));
planet2 = new Planet(70, 332000, new Vector2(400, 400));
I am also aware LibGDX won't have the x, y coordinates of my circle in the middle but rather the bottom left. Therefore I have modified that in the constructor:
this.pos = pos;
this.pos.x -= r;
this.pos.y -= r;
I have been messing around and debugging the code and realised it was a very minor mistake, a classic mistake to assume that the math library's cos() and sin() functions use degrees. They don't. They use radians and that was the whole problem all along.
Instead of:
this.force.x = F * MathUtils.cos(alpha);
this.force.y = F * MathUtils.sin(alpha);
One must do:
this.force.x = F * MathUtils.cosDeg(alpha);
this.force.y = F * MathUtils.sinDeg(alpha);
I will make sure to edit the question to emphasize this problem and solution for future viewers of it.
I would like to rotate an object to face a point which I'm have a bit of of trouble with.
So I'm starting with an object that has a base at zero and is aligned on the y axis.
I would like to rotate it so that the top of the object is facing the destination
My process so far is to:
Given axis A
find the distance between my position and my look position: D
create a direction vector: V = D.normalize()
find the right vector: R = A cross D
find the up vector: U = D cross R
find the angle between up and direction: ANGLE = acos((U dot D) / (U.length * D.length))
rotate by angle scaled by direction on each axis
here is the code representation of that. I'm not sure what exactly is wrong with this I've worked it out on paper and to my knowledge this approach should work but the results are completely incorrect when drawn. If anyone sees any flaws and could point me in the right direction it would be great.
Vector3 distance = new Vector3(from.x, from.y, from.z).sub(to.x, to.y, to.z);
final Vector3 axis = new Vector3(0, 1, 0);
final Vector3 direction = distance.clone().normalize();
final Vector3 right = (axis.clone().cross(direction));
final Vector3 up = (distance.clone().cross(right));
float angle = (float) Math.acos((up.dot(direction)/ (up.length() * direction.length())));
bondObject.rotateLocal(angle, direction.x , direction.y, direction.z);
The basic idea here is as follows.
Determine which way the object is facing: directionA
Determine which way the object should be facing: directionB
Determine the angle between those directions: rotationAngle
Determine the rotation axis: rotationAxis
Here's the modified code.
Vector3 distance = new Vector3(from.x, from.y, from.z).sub(to.x, to.y, to.z);
if (distance.length() < DISTANCE_EPSILON)
{
//exit - don't do any rotation
//distance is too small for rotation to be numerically stable
}
//Don't actually need to call normalize for directionA - just doing it to indicate
//that this vector must be normalized.
final Vector3 directionA = new Vector3(0, 1, 0).normalize();
final Vector3 directionB = distance.clone().normalize();
float rotationAngle = (float)Math.acos(directionA.dot(directionB));
if (Math.abs(rotationAngle) < ANGLE_EPSILON)
{
//exit - don't do any rotation
//angle is too small for rotation to be numerically stable
}
final Vector3 rotationAxis = directionA.clone().cross(directionB).normalize();
//rotate object about rotationAxis by rotationAngle
I've had this old graphics project laying around (written in oberon) and since i wrote it as one of my first projects it looks kinda chaotic.
So I descided that, since i'm bored anyway, i would rewrite it in java.
Everything so far seems to work... Until i try to rotate and/or do my eye-point transformation.
If i ignore said operations the image comes out just fine but the moment i try to do any of the operations that require me to multiply a point with a transformation matrix it all goes bad.
the eye point transformation generates stupidly small numbers with end coördinates like [-0.002027571306540029, 0.05938634628270456, -123.30022583847628]
this causes the resulting image to look empty but if i multiply each point with 1000 it turns out it's just very, very small and, in stead of being rotated, has just been translated in some (seemingly) random direction.
if i then ignore the eye point and simply focus on my rotations the results are also pretty strange (note: the image auto scales depending on the range of coordinates):
setting xRotation to 90° only makes the image very narrow and way too high (resolution should be about 1000x1000 and is then 138x1000
setting yRotation to 90° makes it very wide (1000x138)
setting zRotation to 90° simply seems to translate the image all the way to the right side of the screen.
What i have checked so far:
i have checked and re-checked my rotation matrices at least 15 times now so they are (probably) correct
doing a test multiplication with a vector and the identity matrix does return the original vector
my matrices are initialized as identity matrices prior to being used as rotation matrices
the angles in the files are in degrees but are converted to radian when read.
Having said that i have 2 more notes:
a vector in this case is a simple 3 value array of doubles (representing the x, y and z values)
a matrix is a 4x4 array of doubles initialized as the identity matrix
When trying to rotate them i do it in the order:
scale (multiplying with a scale factor)
rotate along x-axis
rotate along y-axis
rotate along z-axis
translate
do eye-point transformation
then, if the point isn't already on the z-plane, project it
like so:
protected void rotate() throws ParseException
{
Matrix rotate_x = Transformations.x_rotation(rotateX);
Matrix rotate_y = Transformations.y_rotation(rotateY);
Matrix rotate_z = Transformations.z_rotation(rotateZ);
Matrix translate = Transformations.translation(center.x(), center.y(), center.z());
for(Vector3D point : points)
{
point = Vector3D.mult(point, scale);
point = Vector3D.mult(point, rotate_x);
point = Vector3D.mult(point, rotate_y);
point = Vector3D.mult(point, rotate_z);
point = Vector3D.mult(point, translate);
point = Vector3D.mult(point, eye);
if(point.z() != 0)
{
point.setX(point.x()/(-point.z()));
point.setY(point.y()/(-point.z()));
}
checkMinMax(point);
}
}
here's the code that initializes the rotation matrices if you're interested:
public static Matrix eye_transformation(Vector3D eye)throws ParseException
{
double r = eye.length();
double teta = Math.atan2(eye.y(), eye.x());
double zr = eye.z()/r;
double fi = Math.acos(zr);
Matrix v = new Matrix();
v.set(0, 0, -Math.sin(teta));
v.set(0, 1, -Math.cos(teta) * Math.cos(fi));
v.set(0, 2, Math.cos(teta) * Math.sin(fi));
v.set(1, 0, Math.cos(teta));
v.set(1, 1, -Math.sin(teta) * Math.cos(fi));
v.set(1, 2, Math.sin(teta) * Math.sin(fi));
v.set(2, 1, Math.sin(fi));
v.set(2, 2, Math.cos(fi));
v.set(3, 2, -r);
return v;
}
public static Matrix z_rotation(double angle) throws ParseException
{
Matrix v = new Matrix();
v.set(0, 0, Math.cos(angle));
v.set(0, 1, Math.sin(angle));
v.set(1, 0, -Math.sin(angle));
v.set(1, 1, Math.cos(angle));
return v;
}
public static Matrix x_rotation(double angle) throws ParseException
{
Matrix v = new Matrix();;
v.set(1, 1, Math.cos(angle));
v.set(1, 2, Math.sin(angle));
v.set(2, 1, -Math.sin(angle));
v.set(2, 2, Math.cos(angle));
return v;
}
public static Matrix y_rotation(double angle) throws ParseException
{
Matrix v = new Matrix();
v.set(0, 0, Math.cos(angle));
v.set(0, 2, -Math.sin(angle));
v.set(2, 0, Math.sin(angle));
v.set(2, 2, Math.cos(angle));
return v;
}
public static Matrix translation(double a, double b, double c) throws ParseException
{
Matrix v = new Matrix();;
v.set(3, 0, a);
v.set(3, 1, b);
v.set(3, 2, c);
return v;
}
And the actual method that multiplies a point with a rotation matrix
note: NR_DIMS is defined as 3.
public static Vector3D mult(Vector3D lhs, Matrix rhs) throws ParseException
{
if(rhs.get(0, 3)!=0 || rhs.get(1, 3)!=0 || rhs.get(2, 3)!=0 || rhs.get(3, 3)!=1)
throw new ParseException("the matrix multiplificiation thingy just borked");
Vector3D ret = new Vector3D();
double[] vec = new double[NR_DIMS];
double[] temp = new double[NR_DIMS+1];
temp[0] = lhs.x;
temp[1] = lhs.y;
temp[2] = lhs.z;
temp[3] = lhs.infty? 0:1;
for (int i = 0; i < NR_DIMS; i++)
{
vec[i] = 0;
// Multiply the original vector with the i-th column of the matrix.
for (int j = 0; j <= NR_DIMS; j++)
{
vec[i] += temp[j] * rhs.get(j,i);
}
}
ret.x = vec[0];
ret.y = vec[1];
ret.z = vec[2];
ret.infty = lhs.infty;
return ret;
}
I've checked and re-checked this code with my old code (note: the old code works) and it's identical when it comes to the operations.
So I'm at a loss here, I did look around for similar questions but they didn't really provide any useful information.
Thanks :)
small addition:
if i ignore both the eye-point and the rotations (so i only project the image) it comes out perfectly fine.
I can see that the image is complete apart from the rotations.
Any more suggestions?
A few possible mistakes I can think of:
In the constructor of Matrix, you are not loading the identity matrix.
You are passing your angles in degrees instead of radians.
Your eye-projection matrix projects in another range you think? I mean, in OpenGL all projection matrixes should projection onto the rectangle [(-1,-1),(1,1)]. This rectangle represents the screen.
Mixing up premultiply and postmultiply. Id est: I usually do: matrix*vector, where in your code, you seem to be doing vector*matrix, if I'm not mistaken.
Mixing up columns and rows in your Matrix?
I'm going to take another look at your question tomorrow. Hopefully, one of these suggestions helps you.
EDIT: I overlooked you already checked the first two items.
alright, i'm currently feeling like a complete idiot. The issue was a simply logic error.
The error sits in this part of the code:
for(Vector3D point : points)
{
point = Vector3D.mult(point, scale);
point = Vector3D.mult(point, rotate_x);
point = Vector3D.mult(point, rotate_y);
point = Vector3D.mult(point, rotate_z);
point = Vector3D.mult(point, translate);
point = Vector3D.mult(point, eye);
if(point.z() != 0)
{
point.setX(point.x()/(-point.z()));
point.setY(point.y()/(-point.z()));
}
checkMinMax(point);
}
I forgot that, when you obtain an object from a list, it is a new instance of that object with the same data rather than a reference to it.
So what i have done is simply remove the old entry and replace it with the new one.
Problem solved.
I'm trying to write a little game with third-person-camera and I'm just wondering about gluLookAt function. It works with Opengl 1.1, but I'm using 3.2 one so I need something that can return Matrix4f to me, but I didn't find anything on the Internet except some code in C++ and I found it extremely hard to translate it to the LWJGL (their API's are not the same, no sir). For example, I tried to remake this code (This link) :
// ----------------------------------------------------
// View Matrix
//
// note: it assumes the camera is not tilted,
// i.e. a vertical up vector (remmeber gluLookAt?)
//
void setCamera(float posX, float posY, float posZ,
float lookAtX, float lookAtY, float lookAtZ) {
float dir[3], right[3], up[3];
up[0] = 0.0f; up[1] = 1.0f; up[2] = 0.0f;
dir[0] = (lookAtX - posX);
dir[1] = (lookAtY - posY);
dir[2] = (lookAtZ - posZ);
normalize(dir);
crossProduct(dir,up,right);
normalize(right);
crossProduct(right,dir,up);
normalize(up);
float aux[16];
viewMatrix[0] = right[0];
viewMatrix[4] = right[1];
viewMatrix[8] = right[2];
viewMatrix[12] = 0.0f;
viewMatrix[1] = up[0];
viewMatrix[5] = up[1];
viewMatrix[9] = up[2];
viewMatrix[13] = 0.0f;
viewMatrix[2] = -dir[0];
viewMatrix[6] = -dir[1];
viewMatrix[10] = -dir[2];
viewMatrix[14] = 0.0f;
viewMatrix[3] = 0.0f;
viewMatrix[7] = 0.0f;
viewMatrix[11] = 0.0f;
viewMatrix[15] = 1.0f;
setTranslationMatrix(aux, -posX, -posY, -posZ);
multMatrix(viewMatrix, aux);
}
I can understand everything until "float aux[16]", then it just gets messy in my mind, especially in the end.
Can someone make it clear for me? Maybe someone already made "gluLookAt-clone" or something?
EDIT:
Thank you, Brett, now I must understand how to express that in code). You say that "aux" is a matrix, but we give it only 3 floats, so its better be a vector, BUT if it is a vector, so how do I multiply it with 4x4 ViewMatrix? And I cant find a way to just fill Matrix4f with numbers, there is no methods in lib to do that (most likely that because I'm noob and I can't find it, but hey, I really can't)
FINAL EDIT:
Finally I got it to work. I just wasn't understanding full matrix stuff that was required. Here is final working code, if someone interested(I guess not but whatever)). To deal with it, don't forget to setup projection matrix in the begining.
void setCamera(float posX, float posY, float posZ,
float lookAtX, float lookAtY, float lookAtZ) {
Vector3f dir = new Vector3f(lookAtX - posX, lookAtY - posY, lookAtZ - posZ);
Vector3f up = new Vector3f(0, 1f, 0);
Vector3f right = new Vector3f();
dir.normalise();
Vector3f.cross(dir,up,right);
right.normalise();
Vector3f.cross(right,dir,up);
up.normalise();
Matrix4f aux = new Matrix4f();
viewMatrix = new Matrix4f();
viewMatrix.m00 = right.getX();
viewMatrix.m01 = right.getY();
viewMatrix.m02 = right.getZ();
viewMatrix.m03 = 0.0f;
viewMatrix.m10 = up.getX();
viewMatrix.m11 = up.getY();
viewMatrix.m12 = up.getZ();
viewMatrix.m13 = 0.0f;
viewMatrix.m20 = -dir.getX();
viewMatrix.m21 = -dir.getY();
viewMatrix.m22 = -dir.getZ();
viewMatrix.m23 = 0.0f;
viewMatrix.m30 = 0.0f;
viewMatrix.m31 = 0.0f;
viewMatrix.m32 = 0.0f;
viewMatrix.m33 = 1.0f;
//setup aux as a translation matrix by placing positions in the last column
aux.m30 = -posX;
aux.m31 = -posY;
aux.m32 = -posZ;
//multiplication(in fact translation) viewMatrix with aux
Matrix4f.mul(viewMatrix, aux, viewMatrix);
}
I have a first-person camera class that I use (on OpenGL 3.2) which handles movement: x, y and z positions as well as pitch, yaw and roll. The way that I do this is update positions each cycle and a part of rendering I apply these updates from the camera by creating a new view matrix and sending it as a uniform to my vertex shader.
Here is the method that accomplishes this:
#Override
public void applyTranslations(int uniformLocation) {
viewMatrix = new Matrix4f();
Matrix4f.rotate(MatrixUtils.degreesToRadians(pitch), new Vector3f(1, 0, 0), viewMatrix, viewMatrix);
Matrix4f.rotate(MatrixUtils.degreesToRadians(yaw), new Vector3f(0, 1, 0), viewMatrix, viewMatrix);
Matrix4f.rotate(MatrixUtils.degreesToRadians(roll), new Vector3f(0, 0, 1), viewMatrix, viewMatrix);
Matrix4f.translate(new Vector3f(-x, -y, -z), viewMatrix, viewMatrix);
viewMatrix.store(matrix44Buffer); matrix44Buffer.flip();
glUniformMatrix4(uniformLocation, false, matrix44Buffer);
}
Where uniformLocation is the location of my viewMatrix uniform within my shaders.
Steps are to:
Create a new 4x4 matrix
Apply rotations for x, y and z axes
Apply translation for the x, y and z axes
Send matrix to shaders
The code is just populating the matrix as described in the gluLookAt() documentation.
Up until float aux[16], the code is creating an orthonormal basis (3 mutually perpendicular vectors as 'axes'). The properties of orthogonal rotation matrices allow viewMatrix elements to be set directly. aux is then (presumably) populated as a translation matrix, and the transforms are then concatenated with multMatrix.
I'm coding a flocking algorithm in Java but I'm stuck at a certain point (using the Ardor3D libraries, in a 2D plane).
Basically, I need to find the angle difference to add to the current rotation. If you can only get the way it should be pointing with polar coordinates with 0 degs at north and not the difference, not to worry -- I have a method which returns the angle difference taking into account the wraparound on the angle and negative angles.
At the moment, I have the following code, which clearly wouldn't work since the algorithm has no reference to the initial rotation:
long tpf = currUpdateTimeMS - lastUpdateTimeMS;
Vector2 pos = new Vector2();
rt.getPosition(pos);
double rot = pos.angleBetween(app.getAvgBoidPos(new Vector2()).normalizeLocal());
rt.setRotation(rot);
pos.addLocal(
Math.cos((rot - MathUtils.HALF_PI)) * (tpf / 10f),
Math.sin((rot - MathUtils.HALF_PI)) * (tpf / 10f)
);
rt.setPosition(pos);
super.updateLogic();
Updated code (not working, from first answer):
long tpf = currUpdateTimeMS - lastUpdateTimeMS;
//rt.setRotation(rt.getRotation() + ((tpf / (ROT_SPEED / 2f)) % 360));
Vector2 avgpos = app.getAvgBoidPos(new Vector2());
Vector2 pos = rt.getPosition(new Vector2());
avgpos.subtractLocal(pos);
double angleRads = rt.getRotation() * FastMath.DEG_TO_RAD;
double rot = MathUtils.acos((
(avgpos.getX() * MathUtils.sin(angleRads)
) +
(avgpos.getY() * MathUtils.cos(angleRads)
)) / ((Math.pow(avgpos.getX(), 2) + Math.pow(avgpos.getY(), 2)) * 0.5));
double adegdiff = rot * FastMath.RAD_TO_DEG;
rt.setRotation(rt.getRotation() - adegdiff);
double newrot = rt.getRotation();
pos.addLocal(
Math.cos((newrot - MathUtils.HALF_PI)) * (tpf / 10f),
Math.sin((newrot - MathUtils.HALF_PI)) * (tpf / 10f)
);
rt.setPosition(pos);
super.updateLogic();
Another modification based on the other answer:
long tpf = currUpdateTimeMS - lastUpdateTimeMS;
//rt.setRotation(rt.getRotation() + ((tpf / (ROT_SPEED / 2f)) % 360));
Vector2 avgpos = app.getAvgBoidPos(new Vector2());
Vector2 pos = rt.getPosition(new Vector2());
avgpos.subtractLocal(pos);
double rot = pos.angleBetween(
app.getAvgBoidPos(new Vector2()).normalizeLocal()
) - (rt.getRotation() * MathUtils.DEG_TO_RAD);
rt.setRotation(rt.getRotation() - (rot * MathUtils.RAD_TO_DEG));
double newrot = rt.getRotation();
pos.addLocal(
Math.cos((newrot - MathUtils.HALF_PI)) * (tpf / 10f),
Math.sin((newrot - MathUtils.HALF_PI)) * (tpf / 10f)
);
rt.setPosition(pos);
super.updateLogic();
I'm not really too good at Maths problems, so code would be helpful rather than formulas :)
Inputs
Current position of entity
Current rotation of entity (polar-oriented) in degrees
Output
Degrees or radians to add or subtract to current rotation
... or degrees or radians expressed as polar-oriented angle
Thanks in advance if you can help :)
Chris
You can use the dot product to determine the cosine of the angle (in radians) between the current orientation and the point you want to face. Assume the agent doing the viewing is locate at the origin and oriented to face some direction given by the angle θ relative to the Y-Axis (i.e. 0 degrees is "up" or "north"). You want to find the angular difference θ' between that direction and facing a point (x, y). That is given by:
θ' = cos-1[(x*sin(θ) + y*cos(θ)) / sqrt(x2 + y2)]
Subtracting θ' from θ will orient the agent towards the target.
If the agent is not at the origin, simply subtract the position of the agent from the object to view to bring it into the form above.
Slightly off topic, but you might find the particle swarm and wander code in our effects package (ardor3d-effects) interesting as well.
They can be found in the ardor svn, or here:
http://ardorlabs.trac.cvsdude.com/Ardor3Dv1/browser/trunk/ardor3d-effects/src/main/java/com/ardor3d/extension/effect/particle/
heres an implementation on how to find the angle beetween two vectors with a common origin. this has been hacked together based on the algorithm described there:
http://www.wikihow.com/Find-the-Angle-Between-Two-Vectors
public class DeltaDoodle {
private double delta(ColumnVector v1,ColumnVector v2) throws Exception{
double sp=scalarProduct(v1,v2);
double magV1=magnitude(v1);
double magV2=magnitude(v2);
return Math.acos(sp/(magV1*magV2)) * (180/Math.PI);
}
private double scalarProduct(ColumnVector a, ColumnVector b) {
return (a.x*b.x) + (a.y*b.y);
}
private double magnitude(ColumnVector a){
return Math.sqrt((a.x*a.x) + (a.y*a.y));
}
public static void main(String[] args) {
DeltaDoodle v=new DeltaDoodle();
try {
System.out.println("angle: " + v.delta(new ColumnVector(5, 5), new ColumnVector(1,1)));
} catch (Exception e) {
e.printStackTrace();
}
}
}
public class ColumnVector {
public final double x, y;
public ColumnVector(double x1, double x2) {
this.x = x1;
this.y = x2;
}
}
hope that helps...
If I understand these functions correctly, this might just work:
Vector2 pos = new Vector2();
rt.getPosition(pos);
double rot = pos.angleBetween(app.getAvgBoidPos(new Vector2()).normalizeLocal()) - rt.getRotation();
P.S. Forgot to mention: this rot is intended to be the angle difference. Rotate the entity by this much and it should be pointing toward the target.
EDIT:
Thanks, the code does help (I had misconstrued angleBetween). Let me try again:
Here is the vector from the entity to the point (pardon me if I get the syntax wrong, I don't know java):
Vector2 pos = new Vector2();
rt.getPosition(pos);
Vector2 direction = app.getAvgBoidPos(new Vector2());
direction.subtractLocal(pos);
Now we normalize it to get a unit vector pointing toward the point, and take the angle difference:
double rot = rt.getRotation().angleBetween(direction.normalizeLocal())