Develop Reference

How to draw watchface 'ticks' on a square watch?

I currently have this snippet generating the ticks around the outside of and android wear watchface
float innerMainTickRadius = mCenterX - 35;
for(int tickIndex = 0; tickIndex < 12; tickIndex++) {
float tickRot = (float) (tickIndex * Math.PI * 2 / 12);
float innerX = (float) Math.sin(tickRot) * innerMainTickRadius;
float innerY = (float) -Math.cos(tickRot) * innerMainTickRadius;
float outerX = (float) Math.sin(tickRot) * mCenterX;
float outerY = (float) -Math.cos(tickRot) * mCenterX;
canvas.drawLine(mCenterX + innerX, mCenterY + innerY, mCenterX + outerX, mCenterY + outerY, mTickPaint);
}
Which generates the ticks well on a round watchface but on a square it turns out like this:
but I'd like them to not be circular, but instead fit the shape a bit more suitably, e.g:
Is there a standard way to do this? I'm guessing I can't use trig again...

Of course you use geometry and trig. For example any line you put on the clock face you want to point to the center so one part will be the given (x,y) and the other will be arctan2(cy-y,cx-x) giving you the angle from the point you have towards the center (cx,cy) then simply draw the line in the direction of the center of a given length r, by drawing the line from x,y to cos(angle) * r, sin(angle) * r.
However, given your sample image you might want to draw the line from x,y to x+r,y then rotate the canvas by angle so that you can draw those numbers tweaked like that. Be sure to do canvas.save() before tweaking the canvas' matrix and canvas.restore() after the tweak.
This leaves the math of whatever shape you want to draw your ticks from and the positions thereto. You can do this within a Path. So define the path for a rounded rectangle and then use the PathMeasure class to get the getPosTan() and then ignore the tangent and just use the position it gives you to find your position around a rounded rectangle. That or simply calculate those positions as the positions through either a line segment or a bezier section depending on the decided shape.
For example:
static final int TICKS = 12;
static final float TICKLENGTH = 20;
In the draw routine,
float left = cx - 50;
float top = cy - 50;
float right = cx + 50;
float bottom = cy + 50;
float ry = 20;
float rx = 20;
float width = right-left;
float height = bottom-top;
Path path = new Path();
path.moveTo(right, top + ry);
path.rQuadTo(0, -ry, -rx, -ry);
path.rLineTo(-(width - (2 * rx)), 0);
path.rQuadTo(-rx, 0, -rx, ry);
path.rLineTo(0, (height - (2 * ry)));
path.rQuadTo(0, ry, rx, ry);
path.rLineTo((width - (2 * rx)), 0);
path.rQuadTo(rx, 0, rx, -ry);
path.rLineTo(0, -(height - (2 * ry)));
path.close();
PathMeasure pathMeasure = new PathMeasure();
pathMeasure.setPath(path,true);
float length = pathMeasure.getLength();
float[] pos = new float[2];
float r = TICKLENGTH;
for (int i = 0; i < TICKS; i++) {
pathMeasure.getPosTan(i * (length/TICKS),pos,null);
double angle = Math.atan2(cy - pos[1], cx - pos[0]); //yes, y then x.
double cos = Math.cos(angle);
double sin = Math.sin(angle);
canvas.drawLine(pos[0], pos[1], (float)(pos[0] + cos * r), (float)(pos[1] + sin * r), paint);
}
Admittedly it looks like:
So it would take a lot more work to get it looking like your image. But, it's totally doable. The path measure trick thing will work for any shape. I avoided using path.addRoundRect because of the Lollipop+ restriction. You can see my answer to that question here. And the other answers which are plenty fine to how to draw a rounded rectangle-esque shape. You can, if you would like to write an envelope function simply scale your current picture to the envelope of the rectangle according to the factor t, as it goes around the clock.

The angle is a function of the position now. I'm not immediately seeing the trick for getting a closed form in this case. But in the most general case, you could end up just storing the position of each tickmark, then you're just drawing the line that goes through that point and the center. so the angle at second i is just
theta(i)=arctan(y_pos(i) / x_pos(i))
assuming the center has coordinates (0,0). In this case, you only need to store the positions for 8 consecutive ticks because the face is periodic every 90 degrees and symmetric about the diagonals as well.

How to check the touch points of the circles as in the image in Libgdx?

I am facing problem in getting the touch point of the circle for the game i was developing
I tried to solve this by getting the points as below
public Actor hit(float x, float y, boolean touchable){
if(!this.isVisible() || this.getTouchable() == Touchable.disabled)
return null;
// Get center-point of bounding circle, also known as the center of the Rect
float centerX = _texture.getRegionWidth() / 2;
float centerY = _texture.getRegionHeight() / 2;
// Calculate radius of circle
float radius = (float) (Math.sqrt(centerX * centerX + centerY * centerY))-5f;
// And distance of point from the center of the circle
float distance = (float) Math.sqrt(((centerX - x) * (centerX - x))
+ ((centerY - y) * (centerY - y)));
// If the distance is less than the circle radius, it's a hit
if(distance <= radius) return this;
// Otherwise, it isn't
return null;}
I am getting hit positions inside circle but also the points around it near black spots, i only need the touch points near circle.
Would some body suggest the approach for achieving this.

Im guessing that you are comparing local rect coordinates (ie centerX, centerY) with screen coordinates x,y parameters that you are feeding to the function.
So you probably want to subtract the rect's x,y position from the parameters x,y so your parameters are in local coordinates.
So:
float lLocalX = x-rectX (assuming this is the rects x position on the screen)
float lLocalY = y-rectY (assuming this is the rects y position on the screen)
now you can compare them!
float distance = (float) Math.sqrt(((centerX - lLocalX ) * (centerX - lLocalX ))
+ ((centerY - lLocalY ) * (centerY - lLocalY )));

You can have a Circle object in your Actor: http://libgdx.badlogicgames.com/nightlies/docs/api/com/badlogic/gdx/math/Circle.html
Then check if the circle contains that point using the circle.contains(float x, float y) function.
Basically it'll look something like this:
public Actor hit(float x, float y, boolean touchable){
if(!this.isVisible() || this.getTouchable() == Touchable.disabled)
return null;
if (circle.contains(x,y)) return this;
return null;
}
Of course the downside is that if this is a dynamic object and it moves around a lot, then you'd have to constantly update the circles position. Hope this helps :)

Drawing an arrow head in android

I am trying to draw an arrow to point to objects in am image. I have been able to write code to draw the line but cant seem to be able to find a way to draw the arrowhead.The code I wrote to draw a dragabble line is as follows.I need to draw an arrowhead on ACTION_UP event to the direction in which the line is pointing
if(event.getAction() ==MotionEvent.ACTION_DOWN) {
if (count==1){
x1 = event.getX();
y1 = event.getY();
System.out.println(count+"count of value a;skd");
Toast.makeText(getApplicationContext(), ""+(radius+count), Toast.LENGTH_LONG).show();
Log.i(TAG, "coordinate x1 : "+String.valueOf(x1)+" y1 : "+String.valueOf(y1));
}
}
else if(event.getAction() ==MotionEvent.ACTION_MOVE){
imageView.setImageBitmap(bmp2);
x2 = event.getX();
y2 = event.getY();
posX=(float)(x1+x2)/2;
posY=(float)(y1+y2)/2;
radius=(float) Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2))/2;
onDraw();
Toast.makeText(getApplicationContext(), ""+radius, Toast.LENGTH_LONG).show();
}
Hi, for anyone still needing help .This is how I did it in the end
float h=(float) 30.0;
float phi = (float) Math.atan2(y2 - y1, x2 - x1);
float angle1 = (float) (phi - Math.PI / 6);
float angle2 = (float) (phi + Math.PI / 6);
float x3 = (float) (x2 - h * Math.cos(angle1));
float x4 = (float) (x2 - h * Math.cos(angle2));
float y3 = (float) (y2 - h * Math.sin(angle1));
float y4 = (float) (y2 - h * Math.sin(angle2));
c.drawLine(x1, y1,x2,y2 ,pnt);
c.drawLine(x2, y2,x3,y3 ,pnt);
c.drawLine(x2, y2,x4,y4 ,pnt);
I got help from the accepted answer and ios section in stackoverflow

How I would do this is to find the slope of the line, which is drawn between two points(start and end). The slope would be (dy/dx), and that would be a good start point for your arrow. Assuming you want the base of the arrowhead to be perpendicular to the line of the arrow, to find the slope of the base you would find the opposite reciprocal of the slope of the line. for example, lets say that your line has a slope of 2. The slope for the base of your triangle would be (-1/2), because you do (1/(oldslope)) and multiply by -1. I don't know android very well, but if I remember correctly, in Java, you would use a drawPolygon method, and you would have to specify 4 points(3 unique and 1 the same as the first to close it). Given the slope of the base of the tip, we can get our first two points and our final point. You should know before you start the dimensions of the arrowhead you wish to draw, so in this case b will be the length of your baseline. If you take ϴ=arctan(dy/dx), that will give you an angle between the x axis and your baseline. With that ϴ value, you can do ydif = b*sin(ϴ) to get the difference in y value between the two base corners of your arrow. Doing the same thing but with xdif = b*cos(ϴ) gives you the difference in the x value between the two base points. If the location of the final point of the line that the user drew is, say, (x1, y1), then the locations of the basepoints of the triangle would be (x1-(xdif/2), y1-(ydif/2)) and (x1+(xdif/2), y1+(ydif/2)). These two points, p1 and p2, are the first, second, and fourth points in the draw polygon method. To find the third point, we need to find the angle of the original line, by doing ϴ=arctan(dy/dx), this time using your original dy/dx. with that angle. Before we finish the actual calculation of the point, you first have to know how far from the end of your line the tip of the arrow should actually be, in my case, I will use the var h and h = 10. To get the cordinate, (x,y), assuming the cordinate for the line tip is (x1, y1)you would do (x1+hcosϴ, y1+hsinϴ). Use that for the third value in drawPolygon(), and you should be done. sorry if I kind of rushed at the end, I got kind of tired of typing, comment if you need help.

If you managed to draw a line from the input event, you might additionally draw a triangle on its end indicating the direction.
On another project I drew a square everytime a magnetic point on a grid was touched (as you can see here) Sorry I can not provide you any sample code right now. But if that's a suitable approach for you, I might post it later.

Here is a good code, its not mine, It was a Java Graphics2D code that I converted to Canvas. All credit go to the original guy/lady who wrote it
private void drawArrowHead(Canvas canvas, Point tip, Point tail)
{
double dy = tip.y - tail.y;
double dx = tip.x - tail.x;
double theta = Math.atan2(dy, dx);
int tempX = tip.x ,tempY = tip.y;
//make arrow touch the circle
if(tip.x>tail.x && tip.y==tail.y)
{
tempX = (tip.x-10);
}
else if(tip.x<tail.x && tip.y==tail.y)
{
tempX = (tip.x+10);
}
else if(tip.y>tail.y && tip.x==tail.x)
{
tempY = (tip.y-10);
}
else if(tip.y<tail.y && tip.x==tail.x)
{
tempY = (tip.y+10);
}
else if(tip.x>tail.x || tip.x<tail.x)
{
int rCosTheta = (int) ((10)*Math.cos(theta)) ;
int xx = tip.x - rCosTheta;
int yy = (int) ((xx-tip.x)*(dy/dx) + tip.y);
tempX = xx;
tempY = yy;
}
double x, y, rho = theta + phi;
for(int j = 0; j < 2; j++)
{
x = tempX - arrowLength * Math.cos(rho);
y = tempY - arrowLength * Math.sin(rho);
canvas.drawLine(tempX,tempY,(int)x,(int)y,this.paint);
rho = theta - phi;
}
}
Just call this for both sides of your line and it will draw an arrow at each side!

Remap rotation matrix to different axis system

I am using an adapted version of android's getRotationMatrix in a c++ program that reads the phone's sensor data over the network and calculates the device's matrix.
The function works fine and calculates the device's orientation. Unfortunately, Ogre3d has a different axis system than the device. So even though rotation about the x-axis works fine, the y and z axis are wrong. Holding the device level and pointing to north (identity matrix). When I pitch, the rotation is correct. But when I roll and yaw the rotations are alternated. Roll is yaw in Ogre3d and vice versa.
(Ogre3d) ([Device][5])
^ +y-axis ^ +z-axis
* *
* *
* * ^ +y-axis
* * *
* * *
* * *
************> + x-axis ************> +x-axis
*
*
v +z-axis
A quick look at the two axis system looks like Ogre's system (on the left) is essentially the device's system rotated 90 degrees counter clockwise about the x-axis.
I tried to experiment with various combinations when I fist assign sensor values before the matrix is calculated but no combination seems to work correctly. How would I make sure that the rotation matrix getRotationMatrix() produces displays correctly on Ogre3D?
For Reference here is the function that calculates the matrix:
bool getRotationMatrix() {
//sensor data coming through the network are
//stored in accel(accelerometer) and mag(geomagnetic)
//vars which the function has access to
float Ax = accel[0]; float Ay = accel[1]; float Az = accel[2];
float Ex = mag[0]; float Ey = mag[1]; float Ez = mag[2];
float Hx = Ey * Az - Ez * Ay;
float Hy = Ez * Ax - Ex * Az;
float Hz = Ex * Ay - Ey * Ax;
float normH = (float) Math::Sqrt(Hx * Hx + Hy * Hy + Hz * Hz);
if (normH < 0.1f) {
// device is close to free fall (or in space?), or close to
// magnetic north pole. Typical values are > 100.
return false;
}
float invH = 1.0f / normH;
Hx *= invH;
Hy *= invH;
Hz *= invH;
float invA = 1.0f / (float) Math::Sqrt(Ax * Ax + Ay * Ay + Az * Az);
Ax *= invA;
Ay *= invA;
Az *= invA;
float Mx = Ay * Hz - Az * Hy;
float My = Az * Hx - Ax * Hz;
float Mz = Ax * Hy - Ay * Hx;
//ogre3d's matrix3 is column-major whereas getrotatinomatrix produces
//a row-major matrix thus i have tranposed it here
orientation[0][0] = Hx; orientation[0][2] = Mx; orientation[0][2] = Ax;
orientation[1][0] = Hy; orientation[1][3] = My; orientation[1][2] = Ay;
orientation[2][0] = Hz; orientation[2][4] = Mz; orientation[2][2] = Az;
return true;
}

Why not just add the one additional rotation you've already identified before you use it in ogre?

I found the problem. In my function the unit vectors calculated after the cross products I put them in columns whereas I should be putting them in the rows in their appointed matrix3 cells as usual. Something about row-major and column-major confused me even though I was referring to the elements in 2d [][].
multiplying the outcome of the matrix calculation function with this matrix:
1 0 0
0 0 1
0 -1 0
Then pitching the whole result by another p/2 about axis solved the remap problem but I fear my geometry is inverted.

I don't know much about Matrix Rotation, but if the Systems rotates like you are showing, I think that youshould do the following:
X Axis stays the same way, so:
float Ax = accel[0];
float Ex = mag[0];
Y Axis in (Ogre3d) is Z axis in ([Device][5]), so:
float Ay = accel[2];
float Ey = mag[2];
Z Axis in (Ogre3d) is the oposite of Y axis in ([Device][5]), so:
float Az = accel[1] * (-1);
float Ez = mag[1] * (-1);
Try that

Following a straight line (via Path?)

I'm working on a game which will use projectiles. So I've made a Projectile class and a new instance is created when the user touches the screen:
#Override
public boolean onTouch(View v, MotionEvent e){
float touch_x = e.getX();
float touch_y = e.getY();
new Projectile(touch_x, touch_y);
}
And the Projectile class:
public class Projectile{
float target_x;
float target_y;
Path line;
public Projectile(float x, float y){
target_x = x;
target_y = y;
line = new Path();
line.moveTo(MyGame.mPlayerXPos, MyGame.mPlayerYPos);
line.lineTo(target_x, target_y);
}
}
So this makes a Path with 2 points, the player's position and and touch coords. My question is - How can you access points on this line? For example, if I wanted to get the x,y coords of the Projectile at the half point of the line, or the point the Projectile would be at after 100 ticks (moving at a speed of X pixels/tick)?
I also need the Projectile to continue moving after it reaches the final point.. do I need to use line.addPath(line) to keep extending the Path?
EDIT
I managed to get the Projectiles moving in a straight line, but they're going in strange directions. I had to fudge some code up:
private void moveProjectiles(){
ListIterator<Projectile> it = Registry.proj.listIterator();
while ( it.hasNext() ){
Projectile p = it.next();
p.TimeAlive++;
double dist = p.TimeAlive * p.Speed;
float dx = (float) (Math.cos(p.Angle) * dist);
float dy = (float) (Math.sin(p.Angle) * dist);
p.xPos += dx;
p.yPos += -dy;
}
}
The Angle must be the problem.. I'm using this method, which works perfectly:
private double getDegreesFromTouchEvent(float x, float y){
double delta_x = x - mCanvasWidth/2;
double delta_y = mCanvasHeight/2 - y;
double radians = Math.atan2(delta_y, delta_x);
return Math.toDegrees(radians);
}
However, it returns 0-180 for touches above the center of the screen, and 0 to -180 for touches below. Is this a problem?

The best way to model this is with parametric equations. No need to use trig functions.
class Path {
private final float x1,y1,x2,y2,distance;
public Path( float x1, float y1, float x2, float y2) {
this.x1 = x1;
this.y1 = y1;
this.x2 = x2;
this.y2 = y2;
this.distance = Math.sqrt( (x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
}
public Point position( float t) {
return new Point( (1-t)*x1 + t*x2,
(1-t)*y1 + t*y2);
}
public Point position( float ticks, float speed) {
float t = ticks * speed / distance;
return position( t);
}
}
Path p = new Path(...);
// get halfway point
p.position( 0.5);
// get position after 100 ticks at 1.5 pixels per tick
p.position( 100, 1.5);

From geometry, if it's a straight line you can calculate any point on it by using polar coordinates.
If you find the angle of the line:
ang = arctan((target_y - player_y) / (target_x - player_x))
Then any point on the line can be found using trig:
x = cos(ang) * dist_along_line
y = sin(ang) * dist_along_line
If you wanted the midpoint, then you just take dist_along_line to be half the length of the line:
dist_along_line = line_length / 2 = (sqrt((target_y - player_y)^2 + (target_x - player_x)^2)) / 2
If you wanted to consider the point after 100 ticks, moving at a speed of X pixels / tick:
dist_along_line = 100 * X
Hopefully someone can comment on a way to do this more directly using the android libs.

First of all, the Path class is to be used for drawing, not for calculation of the projectile location.
So your Projectile class could have the following attributes:
float positionX;
float positionY;
float velocityX;
float velocityY;
The velocity is calculated from the targetX, targetY, playerX and playerY like so:
float distance = sqrt(pow(targetX - playerX, 2)+pow(targetY - playerY, 2))
velocityX = (targetX - playerX) * speed / distance;
velocityY = (targetY - playerY) * speed / distance;
Your position after 20 ticks is
x = positionX + 20 * velocityX;
y = positionY + 20 * velocityY;
The time it takes to reach terget is
ticksToTarget = distance / velocity;
Location of halp way point is
halfWayX = positionX + velocityX * (tickToTarget / 2);
halfWayY = positionY + velocityY * (tickToTarget / 2);