PureBasic Forum

Procedure.f Rad2degree(Rad.f) 
  myRad.f = (180 * Rad) / #PI
  ProcedureReturn myRad
EndProcedure

;purpose: To calculate the angle between 2 objects in 2D space
;input:    P1 - the location of the first object
;          P2 - the location of the second object
; output: the angle between the objects in degrees
Procedure.f calculateAngle2D(*P1.POINT, *P2.POINT, rad.d)
    Protected  ang.f = 0.0, calc.f = 0.0
    calc = (*P2\y - *P1\y)/ (*P2\x - *P1\x)    ;<--- Error in calculation spottet by Demivec. (Fixed).
    ang = ATan(calc) * radtodeg(rad)
    ;In the event that the angle is in the first quadrant
    If *P2\y < *P1\y And *P2\x > *P1\x
      ProcedureReturn ang
    ElseIf (*P2\y < *P1\y And *P2\x < *P1\x) Or (*P2\y > *P1\y And *P2\x < *P1\x)
    ;In the event of second Or third quadrant
       ProcedureReturn ang + 180
    Else
    ;If none of the above, it must be in the fourth
       ProcedureReturn ang + 360
    EndIf
EndProcedure

Structure _3Dvector
  x.f
  y.f
  z.f
EndStructure

;purpose: To calculate the weight of an object based on its mass
;input:   mass - the mass of the object
;         grav - the amount of constant acceleration due To gravity
;output:  an structure with 3 floats representing the vector of weight
Procedure calcWeight3D(*obj._3Dvector, mass.f, grav.f)
    ;The value in y will be the only number changed, since gravity
    ;is only applied along the Y axis
    ;Calculate the weight, it is assumed that grav(ity) is a negative number
    *obj\y = mass * grav
    ProcedureReturn @Obj
EndProcedure

;Purpose: To find the momentum of object with a given mass,travelling at a certain velocity
Procedure.f momentum(velocity.f, mass.f)
  Protected momentum.f
  momentum = mass*velocity
  ProcedureReturn momentum
EndProcedure

speed*(60/fps))

;Pass velocity And time and return resulting displacement.
Procedure.f calcDisplacement(velocity.f, _time.f)
      ProcedureReturn velocity * _time
EndProcedure

;Pass the old position , velocity And time and return new position specified by time.
Procedure.f calcPosition(oldPosition.f, velocity.f, _time.f)
      ProcedureReturn oldPosition + (velocity * _time)
EndProcedure

Procedure.f calcAvgerageVelocity(_start.f , _End.f, time.f)
      ProcedureReturn (_End - _start)/ time
EndProcedure

;Ohms law procedure
Procedure.f Ohm_Law(value1.f, value2.f, CalcType.i = 0)
  Protected result.f
  Select CalcType
    Case 0     ;Voltage    -     value1 = current : value2 = resistance
      result = value1 * value2
    Case 1     ;Current    -     value1 = voltage : value2 = resistance
      result = value1 / value2
    Case 2     ;Resistance -     value1 = voltage : value2 = current
      result = value1 / value2
  EndSelect
  ProcedureReturn result
EndProcedure

;purpose: To calculate the angle of an object from an arbitrary point (origin) in 2D space
;input:    origin - the location of the origin
;          P1 - the location of the object
;output: the angle from the origin to the object in degrees
Procedure.f calculateRelativeAngle2D(*origin.POINT, *P1.POINT)
  Protected  ang.f, calc.f
  calc = (*P1\y - *origin\y) / (*P1\x - *origin\x)
  ang = Degree(ATan(calc))

  If *P1\y < *origin\y And *P1\x > *origin\x
    ProcedureReturn ang  ;angle is in the first quadrant
  ElseIf (*P1\y < *origin\y And *P1\x < *origin\x) Or (*P1\y > *origin\y And *P1\x < *origin\x)
    ProcedureReturn ang + 180 ;angle is in the second Or third quadrant
  Else
    ProcedureReturn ang + 360 ;angle is in the fourth quadrant
  EndIf
EndProcedure

;first 3 moments of inertia 2D
;   
;   1st moment, center of a mass

;   where
;       sumx + x
;       sum y + y
;   
;    cx = sumx / area
;    cy = sumy / area
;
;   2nd moment, inertia of mass around axis       

;   where
;       sumXX  +  (X*X)
;       sumYY  +  (Y*Y)   
;       sumXY  +  (X*Y)
;   
;   IX = SumXX - (Area * (cx * cx))
;   IY = SumYY - (Area * (cy * cy))
;   IXY = Sumxy - (Area * (cx * cy))
;
;   3rd moments, ra,rb, rc or shape parameter
;   *note the shape parameter is invariant to both scale and rotation for a given identical mass 
;    and can be used to identify shapes in some cases.
 
;   ta= Sqr((2.0 * ix * iY) - (4.0 *( ixy * ixy))/2.0)
;   Ra = (ix + iy) + ta
;   Rb = (ix + iy) - ta
;   Shape = (Ra / Rb)
;
;   orientation of mass   
;   
;       where
;         mmx  = Xmax - Xmin
;         mmy = Ymax - Ymin         
;
;     If ix = iy
;             orient = 45       
;     ElseIf mmx >= mmy     
;             orient = (0.5 * (ATan(2 * (Ixy / (Iy - ix))))) / (#PI / 180)
;     Else
;           orient = (0.5 * (ATan(2 * Ixy / (ix - Iy)))) / (#PI / 180)
;     EndIf

;example below

Structure moments
    ;moments
   ;1st 
    cx.f
    cy.f
    ;2nd
    ix.f
    iy.f
    ixy.f
    ;3rd
    ra.f
    rb.f
    shape.f
    ;orientation
    orient.f 
    ;elipse
    majoraxis.f
    minoraxis.f
    ;bounds
    Xmin.i
    Xmax.i
    Ymin.i
    Ymax.i
 EndStructure
 
Procedure GetMoments(img,x1,x2,y1,y2,color,*mom.moments)
  Protected x,y,px,area.f,sumX.f,sumY.f,sumXX.f,sumYY.f,sumXY.f
  Protected ta.f,mmx.f,mmy.f,cmx.f,cmy.f,orient.f
 
  *mom\Xmin = 99999
  *mom\Ymin = 99999
 
 If StartDrawing(ImageOutput(img))
 
   For x = x1 To x2
       For y = y1 To y2
     
        px = Point(x,y) 
     
         If px = color
           
              sumX + x 
              sumY + y 
              Area + 1   
              sumXX + (x*x)
              sumYY + (y*y) 
              sumXY + (x*y) 
                               
              If x < *mom\Xmin 
                 *mom\Xmin = x
              EndIf
               
              If x > *mom\XMax
                   *mom\Xmax = x
              EndIf
               
              If y < *mom\Ymin 
                 *mom\Ymin = y
              EndIf
               
              If y > *mom\Ymax
                 *mom\Ymax = y
              EndIf
            EndIf
          Next
     Next     
     
     StopDrawing()
     
     ;1st moments cx = centerX cy=centerY
     *mom\cx = sumx / Area
     *mom\cy = sumy / Area
 
     
     ;2nd moments Ix Iy Ixy 
     *mom\ix = SumXX - (Area * (cx * cx))
     *mom\iY = SumYY - (Area * (cy * cy))
     *mom\ixY = Sumxy - (Area * (cx * cy))
                   
     ;3rd moment shape parameter invarent to scale and rotation
     ta= Sqr((2.0 * *mom\ix * *mom\iY) - (4.0 *(*mom\ixy * *mom\ixy)) * 0.5)
           
     *mom\Ra = (*mom\ix + *mom\iy) + ta
     *mom\Rb = (*mom\ix + *mom\iy) - ta
     
     *mom\Shape = (*mom\Ra / *mom\Rb)
       
     mmx = (*mom\Xmax - *mom\Xmin)
     mmy = (*mom\Ymax - *mom\Ymin)
     cmx = (*mom\Xmax + *mom\Xmin) * 0.5
     cmy = (*mom\Ymax + *mom\Ymin) * 0.5
     dmx = *mom\cx - cmx
     dmy = *mom\cy - cmy
                   
     ;orientation       
      If *mom\ix = *mom\iy
             orient = 45       
      ElseIf mmx >= mmy
             orient = (0.5 * (ATan(2 * (*mom\Ixy / (*mom\iy - *mom\ix))))) / (#PI / 180)
             *mom\majoraxis = (mmx / Cos(Abs(orient) / (180 / #PI))) * 0.5
             *mom\minoraxis = (Area) / (#PI * *mom\majoraxis)
      Else
             orient = (0.5 * (ATan(2 * *mom\Ixy / (*mom\ix - *mom\Iy)))) / (#PI / 180)
             *mom\majoraxis = (mmy / Cos(Abs(orient) / (180 / #PI))) * 0.5
             *mom\minoraxis = (Area) / (#PI * *mom\majoraxis)
      EndIf
         
      If mmx = mmy  And Abs(*mom\ix- *mom\iy) < 1000
             orient = 0
      EndIf
     
      ;messy fudge to output  0 to 360 degrees
      If *mom\ixy > 0
           If *mom\iy > *mom\ix
                If dmx > dmy
                   orient = (360 + orient) / (180/#PI)
                Else
                   orient = (180 + orient) / (180/#PI)
                EndIf
             Else
                If dmx > dmy
                  orient = (90 - orient) / (180/#PI)
                Else
                  orient = (270 - orient) / (180/#PI)
                EndIf 
             EndIf
          Else
             If *mom\iy > *mom\ix
                If dmy > dmx
                  orient = (180 + orient) / (180/#PI)
                Else
                  orient = orient / (180/#PI)
                EndIf   
             Else
                If dmx > dmy
                  orient = (90 - orient) / (180/#PI)
                Else
                  orient = (270 - orient) / (180/#PI)
                EndIf   
             EndIf
        EndIf   
                   
      If orient < 0
            orient = 0
      EndIf     
     
      *mom\orient = orient
     
   EndIf   
         
 EndProcedure   

Procedure.f Frac(a.f)
   result.f = a.f - Round(a.f,#PB_Round_Down)
   ProcedureReturn result.f
EndProcedure

Debug frac(2003.5)