Develop Reference

Scale, rotate, translate w. matrices in openGl ES 2.0

I'm working with OpenGL ES 2.0 and trying to build my object class with some methods to rotate/translate/scale them.
I just set up my object in 0,0,0 and move it afterwards to the desired position on the screen. Below are my methods to move it seperately. After that i run the buildObjectModelMatrix to pass all the matrices into one objectMatrix, so i can take the vertices and multiply them with my modelMatrix/objectMatrix and render it afterwards.
What i think is right, i have to multiply my matrices in this order:
[scale]x[rotation]x[translation]
->
[temp]x[translation]
->
[objectMatrix]
I've found some literature. Maybe i get it in a few Minutes, if i will, i will update it.
Beginning Android 3D
http://gamedev.stackexchange.com
setIdentityM(scaleMatrix, 0);
setIdentityM(translateMatrix, 0);
setIdentityM(rotateMatrix, 0);
public void translate(float x, float y, float z) {
translateM(translateMatrix, 0, x, y, z);
buildObjectModelMatrix();
}
public void rotate(float angle, float x, float y, float z) {
rotateM(rotateMatrix, 0, angle, x, y, z);
buildObjectModelMatrix();
}
public void scale(float x, float y,float z) {
scaleM(scaleMatrix, 0, x, y, z);
buildObjectModelMatrix();
}
private void buildObjectModelMatrix() {
multiplyMM(tempM, 0, scaleMatrix, 0, rotateMatrix, 0);
multiplyMM(objectMatrix, 0, tempM, 0, translateMatrix, 0);
}
SOLVED:
The Problem within the whole thing is, if you scale before you translate you get a difference in the distance you translate! the correct code for multiplying your matrices should be (correct me if i'm wrong)
private void buildObjectModelMatrix() {
multiplyMM(tempM, 0, translateMatrix, 0, rotateMatrix, 0);
multiplyMM(objectMatrix, 0, tempM, 0, scaleMatrix, 0);
}
with this you translate and rotate first. Afterwards you can scale the object.
Tested with multiple Objects... so i hope this helped :)

You know this is the most common issue with most people when beginning to deal with matrix operations. How matrix multiplication works is as if you were looking from the objects first person view getting some commands: For instance if you began at (0,0,0) facing toward positive X axis and up would be positive Y axis then translate (a,0,0) would mean "go forward", translate (0,0,a) would would mean "go left", rotate (a, 0, 1, 0) would mean "turn left"...
So if in your case you scaled by 3 units, rotated by 90 degrees and then translated by (2,0,0) what happens is you first enlarge yourself by scale of 3, then turn 90 degrees so you are now facing positive Z still being quite large. Then you go forward by 2 units measured in your own coordinate system which means you will actually go to (0,0,2*3). So you end up at (0,0,6) looking toward positive Z axis.
I believe this way is the best to be able to imagine what goes on when dealing with such operations. And might save your life when having a bug in matrix operation order.
You should know that although this kind of matrix operating is normal when beginning with a 3D scene you should try to move to a better system as soon as possible. What I mostly use is to have an object structure/class which contains 3 vectors: position, forward and up (this is much like using glLookAt but not totally the same). So when having these 3 vectors you can simply set a specific position or rotation using trigonometry or your matrix tools by multiplying the vectors with matrices instead of the matrices with matrices. Or you can work with them internally (first person) where for instance "go forward" would be done as position = position + position*forward*scale, turn left would be rotating a forward vector around the up vector. Anyway I hope can understand how to manipulate those 3 vectors to get a desired effect... So what you need to do to reconstruct the matrix from those 3 vector is need to generate another vector right which is a cross product of up and forward then the model matrix consists of:
right.x, right.y, right.z, .0
up.x, up.y, up.z, .0
forward.x, forward.y, forward.z, .0
position.x, position.y, position.z, 1.0
Just note the row-column order may change depending on what you are working with.
I hope this gives you some better understanding...

Strange Matrix transformation for SVG rotate

I have a java code for SVG drawing. It processes transforms including rotate, and does this very well, as far as I can see in numerous test pictures compared against their rendering in Chrome. Next what I need is to get actual object location, which is in many images declared via transforms. So I decided just to read X and Y from Matrix used for drawing. Unfortunately I get incorrect values for rotate transform, that is they do not correspond to real object location in the image.
The stripped down code looks like this:
Matrix matrix = new Matrix();
float cx = 1000; // suppose this is an object X coordinate
float cy = 300; // this is its Y coordinate
float angle = -90; // rotate counterclockwise, got from "rotate(-90, 1000, 300)"
// shift to -X,-Y, so object is in the center
matrix.postTranslate(-cx, -cy);
// rotate actually
matrix.postRotate(angle);
// shift back
matrix.postTranslate(cx, cy);
// debug goes here
float[] values = new float[9];
matrix.getValues(values);
Log.v("HELLO", values[Matrix.MTRANS_X] + " " + values[Matrix.MTRANS_Y]);
The log outputs the values 700 and 1300 respectively. I'd expect 0 and 0, because I see the object rotated inplace in my image (that is there is no any movement), and postTranslate calls should compensate each other. Of course, I see how these values are formed from 1000 and 300, but don't understand why. Once again, I point out that the matrix with these strange values is used for actual object drawing, and it looks correct. Could someone explain what happens here? Am I missing something? So far I have only one solution of my problem: just do not try to obtain position from rotate, do it only for explicit matrix and translate transforms. But this approach lacks generality, and anyway I thought matrix should have reasonable values (including offsets) for any transformation type.

The answer is that the matrix is an operator for space transformation, and should not be used for direct extraction of object position. Instead, one should get initial object coordinates, as specified in x and y attributes of an SVG tag, and apply the matrix on them:
float[] src = new float[2];
src[0] = cx;
src[1] = cy;
matrix.mapPoints(src);
After this we get proper location values in x and y variables.

Detect touch on OpenGL object?

I am developing an application which uses OpenGL for rendering of the images.
Now I just want to determine the touch event on the opengl sphere object which I have drwn.
Here i draw 4 object on the screen. now how should I come to know that which object has been
touched. I have used onTouchEvent() method. But It gives me only x & y co-ordinates but my
object is drawn in 3D.
please help since I am new to OpenGL.
Best Regards,
~Anup

t Google IO there was a session on how OpenGL was used for Google Body on Android. The selecting of body parts was done by rendering each of them with a solid color into a hidden buffer, then based on the color that was on the touch x,y the corresponding object could be found. For performance purposes, only a small cropped area of 20x20 pixels around the touch point was rendered that way.

Both approach (1. hidden color buffer and 2. intersection test) has its own merit.
1. Hidden color buffer: pixel read-out is a very slow operation.
Certainly an overkill for a simple ray-sphere intersection test.
Ray-sphere intersection test: this is not that difficult.
Here is a simplified version of an implementation in Ogre3d.
std::pair<bool, m_real> Ray::intersects(const Sphere& sphere) const
{
const Ray& ray=*this;
const vector3& raydir = ray.direction();
// Adjust ray origin relative to sphere center
const vector3& rayorig = ray.origin() - sphere.center;
m_real radius = sphere.radius;
// Mmm, quadratics
// Build coeffs which can be used with std quadratic solver
// ie t = (-b +/- sqrt(b*b + 4ac)) / 2a
m_real a = raydir%raydir;
m_real b = 2 * rayorig%raydir;
m_real c = rayorig%rayorig - radius*radius;
// Calc determinant
m_real d = (b*b) - (4 * a * c);
if (d < 0)
{
// No intersection
return std::pair<bool, m_real>(false, 0);
}
else
{
// BTW, if d=0 there is one intersection, if d > 0 there are 2
// But we only want the closest one, so that's ok, just use the
// '-' version of the solver
m_real t = ( -b - sqrt(d) ) / (2 * a);
if (t < 0)
t = ( -b + sqrt(d) ) / (2 * a);
return std::pair<bool, m_real>(true, t);
}
}
Probably, a ray that corresponds to cursor position also needs to be calculated. Again you can refer to Ogre3d's source code: search for getCameraToViewportRay. Basically, you need the view and projection matrix to calculate a Ray (a 3D position and a 3D direction) from 2D position.

In my project, the solution I chose was:
Unproject your 2D screen coordinates to a virtual 3D line going through your scene.
Detect possible intersections of that line and your scene objects.
This is quite a complex tast.

I have only done this in Direct3D rather than OpenGL ES, but these are the steps:
Find your modelview and projection matrices. It seems that OpenGL ES has removed the ability to retrieve the matrices set by gluProject() etc. But you can use android.opengl.Matrix member functions to create these matrices instead, then set with glLoadMatrix().
Call gluUnproject() twice, once with winZ=0, then with winZ=1. Pass the matrices you calculated earlier.
This will output a 3d position from each call. This pair of positions define a ray in OpenGL "world space".
Perform a ray - sphere intersection test on each of your spheres in order. (Closest to camera first, otherwise you may select a sphere that is hidden behind another.) If you detect an intersection, you've touched the sphere.

for find touch point is inside circle or not..
public boolean checkInsideCircle(float x,float y, float centerX,float centerY, float Radius)
{
if(((x - centerX)*(x - centerX))+((y - centerY)*(y - centerY)) < (Radius*Radius))
return true;
else
return false;
}
where
1) centerX,centerY are center point of circle.
2) Radius is radius of circle.
3) x,y point of touch..

First Person Camera rotation in 3D

I have written a first person camera class for android.
The class is really simple , the camera object has its three axes
X,y and Z
and there are functions to create the ModelView matrix ( i.e. calculateModelViewMatrix() ),
rotate the camera along its X and Y axis
and Translate the camera along its Z-axis.
I think that my ModelViewMatrix calulation is correct and i can also translate the camera along the Z-axis.
Rotation along x-axis seems to work but along Y-axis it gives strange results.
Also another problem with the rotation seems to be that instead of the camera being rotated, my 3d model starts to rotate instead along its axis.
I have written another implementation based on the look at point and using the openGL ES's GLU.gluLookAt( ) function to obtain the ModelView matrix but that too seems to suffer from the exactly the same problems.
EDIT
First of all thanks for your reply.
I have actually made a second implementation of the Camera class, this time using the rotation functions provided in android.opengl.Matrix class as you said.
I have provided the code below, which is much simpler.
To my surprise, the results are "Exactly" the same.
This means that my rotation functions and Android's rotation functions are producing the same results.
I did a simple test and looked at my data.
I just rotated the LookAt point 1-dgree at a time around Y-axis and looked at the coordinates. It seems that my LookAt point is lagging behind the exact rotation angle e.g. at 20-deg it has only roatated 10 to 12 degree.
And after 45-degrees it starts reversing back

There is a class android.opengl.Matrix which is a collection of static methods which do everything you need on a float[16] you pass in. I highly recommend you use those functions instead of rolling your own. You'd probably want either setLookAtM with the lookat point calculated from your camera angles (using sin, cos as you are doing in your code - I assume you know how to do this.)
-- edit in response to new answer --
(you should probably have edited your original question, by the way - your answer as another question confused me for a bit)
Ok, so here's one way of doing it. This is uncompiled and untested. I decided to build the matrix manually instead; perhaps that'll give a bit more information about what's going on...
class TomCamera {
// These are our inputs - eye position, and the orientation of the camera.
public float mEyeX, mEyeY, mEyeZ; // position
public float mYaw, mPitch, mRoll; // euler angles.
// this is the outputted matrix to pass to OpenGL.
public float mCameraMatrix[] = new float [16];
// convert inputs to outputs.
public void createMatrix() {
// create a camera matrix (YXZ order is pretty standard)
// you may want to negate some of these constant 1s to match expectations.
Matrix.setRotateM(mCameraMatrix, 0, mYaw, 0, 1, 0);
Matrix.rotateM(mCameraMatrix, 0, mPitch, 1, 0, 0);
Matrix.rotateM(mCameraMatrix, 0, mRoll, 0, 0, 1);
Matrix.translateM(mCameraMatrix, 0, -mEyeX, -mEyeY, -mEyeZ);
}
}

How can I tell if a closed path contains a given point?

In Android, I have a Path object which I happen to know defines a closed path, and I need to figure out if a given point is contained within the path. What I was hoping for was something along the lines of
path.contains(int x, int y)
but that doesn't seem to exist.
The specific reason I'm looking for this is because I have a collection of shapes on screen defined as paths, and I want to figure out which one the user clicked on. If there is a better way to be approaching this such as using different UI elements rather than doing it "the hard way" myself, I'm open to suggestions.
I'm open to writing an algorithm myself if I have to, but that means different research I guess.

Here is what I did and it seems to work:
RectF rectF = new RectF();
path.computeBounds(rectF, true);
region = new Region();
region.setPath(path, new Region((int) rectF.left, (int) rectF.top, (int) rectF.right, (int) rectF.bottom));
Now you can use the region.contains(x,y) method.
Point point = new Point();
mapView.getProjection().toPixels(geoPoint, point);
if (region.contains(point.x, point.y)) {
// Within the path.
}
** Update on 6/7/2010 **
The region.setPath method will cause my app to crash (no warning message) if the rectF is too large. Here is my solution:
// Get the screen rect. If this intersects with the path's rect
// then lets display this zone. The rectF will become the
// intersection of the two rects. This will decrease the size therefor no more crashes.
Rect drawableRect = new Rect();
mapView.getDrawingRect(drawableRect);
if (rectF.intersects(drawableRect.left, drawableRect.top, drawableRect.right, drawableRect.bottom)) {
// ... Display Zone.
}

The android.graphics.Path class doesn't have such a method. The Canvas class does have a clipping region that can be set to a path, there is no way to test it against a point. You might try Canvas.quickReject, testing against a single point rectangle (or a 1x1 Rect). I don't know if that would really check against the path or just the enclosing rectangle, though.
The Region class clearly only keeps track of the containing rectangle.
You might consider drawing each of your regions into an 8-bit alpha layer Bitmap with each Path filled in it's own 'color' value (make sure anti-aliasing is turned off in your Paint). This creates kind of a mask for each path filled with an index to the path that filled it. Then you could just use the pixel value as an index into your list of paths.
Bitmap lookup = Bitmap.createBitmap(width, height, Bitmap.Config.ALPHA_8);
//do this so that regions outside any path have a default
//path index of 255
lookup.eraseColor(0xFF000000);
Canvas canvas = new Canvas(lookup);
Paint paint = new Paint();
//these are defaults, you only need them if reusing a Paint
paint.setAntiAlias(false);
paint.setStyle(Paint.Style.FILL);
for(int i=0;i<paths.size();i++)
{
paint.setColor(i<<24); // use only alpha value for color 0xXX000000
canvas.drawPath(paths.get(i), paint);
}
Then look up points,
int pathIndex = lookup.getPixel(x, y);
pathIndex >>>= 24;
Be sure to check for 255 (no path) if there are unfilled points.

WebKit's SkiaUtils has a C++ work-around for Randy Findley's bug:
bool SkPathContainsPoint(SkPath* originalPath, const FloatPoint& point, SkPath::FillType ft)
{
SkRegion rgn;
SkRegion clip;
SkPath::FillType originalFillType = originalPath->getFillType();
const SkPath* path = originalPath;
SkPath scaledPath;
int scale = 1;
SkRect bounds = originalPath->getBounds();
// We can immediately return false if the point is outside the bounding rect
if (!bounds.contains(SkFloatToScalar(point.x()), SkFloatToScalar(point.y())))
return false;
originalPath->setFillType(ft);
// Skia has trouble with coordinates close to the max signed 16-bit values
// If we have those, we need to scale.
//
// TODO: remove this code once Skia is patched to work properly with large
// values
const SkScalar kMaxCoordinate = SkIntToScalar(1<<15);
SkScalar biggestCoord = std::max(std::max(std::max(bounds.fRight, bounds.fBottom), -bounds.fLeft), -bounds.fTop);
if (biggestCoord > kMaxCoordinate) {
scale = SkScalarCeil(SkScalarDiv(biggestCoord, kMaxCoordinate));
SkMatrix m;
m.setScale(SkScalarInvert(SkIntToScalar(scale)), SkScalarInvert(SkIntToScalar(scale)));
originalPath->transform(m, &scaledPath);
path = &scaledPath;
}
int x = static_cast<int>(floorf(point.x() / scale));
int y = static_cast<int>(floorf(point.y() / scale));
clip.setRect(x, y, x + 1, y + 1);
bool contains = rgn.setPath(*path, clip);
originalPath->setFillType(originalFillType);
return contains;
}

I know I'm a bit late to the party, but I would solve this problem by thinking about it like determining whether or not a point is in a polygon.
http://en.wikipedia.org/wiki/Point_in_polygon
The math computes more slowly when you're looking at Bezier splines instead of line segments, but drawing a ray from the point still works.

For completeness, I want to make a couple notes here:
As of API 19, there is an intersection operation for Paths. You could create a very small square path around your test point, intersect it with the Path, and see if the result is empty or not.
You can convert Paths to Regions and do a contains() operation. However Regions work in integer coordinates, and I think they use transformed (pixel) coordinates, so you'll have to work with that. I also suspect that the conversion process is computationally intensive.
The edge-crossing algorithm that Hans posted is good and quick, but you have to be very careful for certain corner cases such as when the ray passes directly through a vertex, or intersects a horizontal edge, or when round-off error is a problem, which it always is.
The winding number method is pretty much fool proof, but involves a lot of trig and is computationally expensive.
This paper by Dan Sunday gives a hybrid algorithm that's as accurate as the winding number but as computationally simple as the ray-casting algorithm. It blew me away how elegant it was.
See https://stackoverflow.com/a/33974251/338479 for my code which will do point-in-path calculation for a path consisting of line segments, arcs, and circles.