Pre-requisite:

1. Polar and Cartesian Coordinates

Objectives:

1. To demonstrate an object launch to a target point

Descriptions:

1. To move your object towards a location,provided targeted location and current location, you can suppose your current location origin and then get the relative position of the target location in polar coordinate.
2. This will give you the direction you need to travel.
3. Given the speed you want the object to travel,

4. Stepped example : (Click mouse to step, Hold down to see the hint, More content under demo 1, please scroll down to view Keynote 0)

   Source

    
   final int appwidth = 600;
   final int appheight = 600;
   final float stepsize = 10;
   targetedobject myobject;
   class targetedobject {  // This is the object to move
     int mcurrentx, mcurrenty;  // This will store the current location of the object
     int mtargetx, mtargety;    // This will store the target location of the object
     int mtargetx_t, mtargety_t;  // Step travel
     float mrotation;      // This is the current orientation of this object
     float thisstep;
     boolean demostep;
     targetedobject( int x, int y, int r ) {  // Initialize with coordinate and orientation
       mcurrentx = x;
       mtargetx = x;
       mcurrenty = y;
       mtargety = y;
       mrotation = r;
       demostep = false;
     }
     void updatedraw() {  //Draws the shape
       pushMatrix();
       translate( mcurrentx, mcurrenty );
       rotate( mrotation );
       noStroke();
       fill( 255, 0, 0 );
       ellipse(0, 0, 40, 40);
       noFill();
       stroke(255);
       strokeWeight(5);
       line( -10, 0, 10, 0 );
       line( 10, 0, 5, -5 );
       line( 10, 0, 5, 5 );
       popMatrix();
       this.drawhelper();
     }
     void drawhelper() {
       if ( this.demostep ) {  //Need draw
         float textx, texty;
         noFill();
         strokeWeight(3);
         stroke( 0, 255, 255, 192 );
         line( this.mcurrentx, this.mcurrenty, this.mtargetx, this.mtargety );
         line( this.mtargetx, this.mcurrenty, this.mtargetx, this.mtargety );
         line( this.mcurrentx, this.mcurrenty, this.mtargetx, this.mcurrenty );
         textSize(24);
         textAlign(CENTER, BOTTOM);
         noStroke();
         fill(255);
         textx = (this.mtargetx + this.mcurrentx) / 2;
         texty = this.mcurrenty;
         text( "X2 - X1", textx, texty );
         textAlign(LEFT, CENTER);
         textx = this.mtargetx;
         texty = (this.mtargety + this.mcurrenty) / 2;
         text( "Y2 - Y1", textx, texty );
         textAlign(CENTER, CENTER);
         textx = (this.mtargetx + this.mcurrentx) / 2;
         texty = (this.mtargety + this.mcurrenty) / 2;
         text( "L", textx, texty );
         
         noFill();
         strokeWeight(3);
         stroke(255,0,0);
         arc( this.mcurrentx, this.mcurrenty, 64, 64, 0, this.mrotation );
         textx = this.mcurrentx + 40;
         texty = this.mcurrenty + 40;
         text( degrees(this.mrotation), textx, texty );
       }
     }
     void startstep(int x, int y) {
       float targetlength;
       float temprotation;
       this.demostep = true;
       this.mtargetx = x;
       this.mtargety = y;
       targetlength = sqrt( pow( this.mtargetx - this.mcurrentx, 2 ) + 
         pow(  this.mtargety - this.mcurrenty, 2 ) );  //Get the target distance
       if (targetlength <= 0.5) {
         this.mrotation = 0;
         return;  //Do not move
       }
       if (targetlength > stepsize) {  //Calculate step size
         this.thisstep = stepsize;
       }
       else {
         this.thisstep = targetlength;
       }
       temprotation = acos( (this.mtargetx - this.mcurrentx) / targetlength );
       if ( this.mtargety > this.mcurrenty ) {  //> 180 degrees
         this.mrotation = temprotation;
       }else{
         this.mrotation = 2 * PI - temprotation;
       }
       // Calculate the step target
       this.mtargetx_t = (int)(this.thisstep * cos(this.mrotation));
       this.mtargety_t = (int)(this.thisstep * sin(this.mrotation));
     }
     void endstep() {
       this.demostep = false;
       this.mcurrentx += this.mtargetx_t;
       this.mcurrenty += this.mtargety_t;
     }
   }
   void setup() {
     size(appwidth, appheight);
     background(0);
     myobject = new targetedobject( width / 2, height / 2, 0 );
   }
   void draw() {
     background(0);
     myobject.updatedraw();
   }
   void mousePressed() {
     if (mouseButton == LEFT) {
       myobject.startstep(mouseX, mouseY);
     }
   }
   void mouseReleased() {
     if ( myobject.demostep ) {
       myobject.endstep();
     }
   }
   

5. Key note

    
   //Get the target distance
   targetlength = sqrt( pow( this.mtargetx - this.mcurrentx, 2 ) + 
                        pow( this.mtargety - this.mcurrenty, 2 ) );
    
   //Arc cosin adjacent side divide by Hypotenuse
   //OR arc sin subtense divide by Hypotenuse
   //Not using tangent to avoid Divide by Zero
   temprotation = acos( (this.mtargetx - this.mcurrentx) / targetlength );
    
   //In this case, we are using cosin, so for the angle > 180 which means that
   //targety is under currend y
   if ( this.mtargety > this.mcurrenty ) {  //> 180 degrees
       this.mrotation = temprotation;
   }else{
       this.mrotation = 2 * PI - temprotation;
   }
    
   //Now that we have the rotation, we recalculate the x and y we need to travel
   this.mtargetx_t = (int)(this.thisstep * cos(this.mrotation));
   this.mtargety_t = (int)(this.thisstep * sin(this.mrotation));
   
    
   //Finally, move the object
   this.mcurrentx += this.mtargetx_t;
   this.mcurrenty += this.mtargety_t;