Math Routines #1

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Teasy	Created : 21 August 2007 Edited : 21 August 2007 Language : Blitz Math Routines #1 Collection of handy functions for various purposes such as trigonometry.
- very fast for imprecise trigonometry Function qSin#( Value% ) Function qCos#( Value% ) - polar & cartesian coordinate conversion routines Function VectorX# ( Distance# , Angle# ) Function VectorY# ( Distance# , Angle# ) Function VectorDistance# ( X# , Y# ) Function VectorAngle# ( X# , Y# ) - short hand Function vx# ( d# , a# ) Return Sin ( a ) * d End Function Function vy# ( d# , a# ) Return Sin ( a - 90 ) * d End Function Function vd# ( x# , y# ) Return Sqr ( x * x + y * y ) End Function Function va# ( x# , y# ) Return -ATan2 ( x , y ) + 180 End Function - quick and imprecise Function qvx# ( d# , a# ) Return qSin ( a ) * d End Function Function qvy# ( d# , a# ) Return qSin ( a - 90 ) * d End Function - Range limiting (overflow) Function RangeFloat#( Value# , Max#=360 ) Function RangeInt%( Value% , Max%=360 ) - Capping (no overflow) Function CapFloat#( Value# , Min#,Max# ) Function CapInt%( Value% , Min%,Max% ) - Comparison Function HighestFloat#( Value1# , Value2# ) Function HighestInt%( Value1% , Value2% ) Function LowestFloat#( Value1# , Value2# ) Function LowestInt%( Value1% , Value2% ) - Step limiting (interleaving) Function InterleaveInt%( Angle% , RotationInterval%=5,Angles%=360 ) - Angles Function AngleDifference( CurrentAngle , TargetAngle ) Function InterceptAngle( ex#,ey# , evx#,evy# , px#,py# , pvx#,pvy# , bs# , maxtime=0 ) - Collision Function PointInRect( px,py , rx,ry , w,h ) ;------------------------------------------------------------------------------- ; * Mathematical Routines ; Ver 2007 Apr 27 Rev 1 ;------------------------------------------------------------------------------- ; This library auto-initializes ; Note: Some of these functions are NOT backward compatible with pre-2007 code ; Sine / Cosine tables Global Math_SinTable#[ 360 ] Global Math_CosTable#[ 360 ] Function Math_InitTables() Local Angle For Angle = 0 To 360 Math_SinTable[ Angle ] = Sin( Angle ) Math_CosTable[ Angle ] = Cos( Angle ) Next End Function Math_InitTables ; Wrapper functions; very fast for imprecise trigonometry Function qSin#( Value% ) If Value < 0 Then Return Math_SinTable[ 360 - Abs( Value ) Mod 360 ] If Value >= 360 Then Return Math_SinTable[ Value Mod 360 ] Return Math_SinTable[ Value ] End Function Function qCos#( Value% ) If Value < 0 Then Return Math_CosTable[ 360 - Abs( Value ) Mod 360 ] If Value >= 360 Then Return Math_CosTable[ Value Mod 360 ] Return Math_CosTable[ Value ] End Function ; Vectors / trigonometry ; polar & cartesian coordinate conversion routines Function VectorX# ( Distance# , Angle# ) Return Sin ( Angle ) * Distance End Function Function VectorY# ( Distance# , Angle# ) Return Sin ( Angle - 90 ) * Distance End Function Function VectorDistance# ( X# , Y# ) Return Sqr ( X * X + Y * Y ) End Function Function VectorAngle# ( X# , Y# ) Return -Atan2 ( X , Y ) + 180 End Function ; short hand Function vx# ( d# , a# ) Return Sin ( a ) * d End Function Function vy# ( d# , a# ) Return Sin ( a - 90 ) * d End Function Function vd# ( x# , y# ) Return Sqr ( x * x + y * y ) End Function Function va# ( x# , y# ) Return -ATan2 ( x , y ) + 180 End Function ; quick and imprecise Function qvx# ( d# , a# ) Return qSin ( a ) * d End Function Function qvy# ( d# , a# ) Return qSin ( a - 90 ) * d End Function ; Range limiting (overflow) Function RangeFloat#( Value# , Max#=360 ) If Value < 0 Then Return Max - Abs( Value ) Mod Max If Value >= Max Then Return Value Mod Max Return Value End Function Function RangeInt%( Value% , Max%=360 ) If Value < 0 Then Return Max - Abs( Value ) Mod Max If Value >= Max Then Return Value Mod Max Return Value End Function ; Capping (no overflow) Function CapFloat#( Value# , Min#,Max# ) If Value < Min Then Return Min If Value > Max Then Return Max Return Value End Function Function CapInt%( Value% , Min%,Max% ) If Value < Min Then Return Min If Value > Max Then Return Max Return Value End Function ; Comparison Function HighestFloat#( Value1# , Value2# ) If Value1 > Value2 Return Value1 Else Return Value2 EndIf End Function Function HighestInt%( Value1% , Value2% ) If Value1 > Value2 Return Value1 Else Return Value2 EndIf End Function Function LowestFloat#( Value1# , Value2# ) If Value1 < Value2 Return Value1 Else Return Value2 EndIf End Function Function LowestInt%( Value1% , Value2% ) If Value1 < Value2 Return Value1 Else Return Value2 EndIf End Function ; Step limiting (interleaving) Function InterleaveInt%( Angle% , RotationInterval%=5,Angles%=360 ) Return Int( Float( RangeInt( Angle,Angles ) - RotationInterval ) / RotationInterval ) * RotationInterval + RotationInterval End Function ; Angles ; return relative angle difference (takes angle wrapping into account) ; - max angle difference: 359 degrees Function AngleDifference( CurrentAngle , TargetAngle ) If TargetAngle - CurrentAngle > 180 Then TargetAngle = TargetAngle - 360 If CurrentAngle - TargetAngle > 180 Then CurrentAngle = CurrentAngle - 360 Return CurrentAngle - TargetAngle End Function ; calculate intelligent hit angle with constant object and projectile speed Const Math_InterceptAngle_OutOfRange = -1001 Function InterceptAngle( ex#,ey# , evx#,evy# , px#,py# , pvx#,pvy# , bs# , maxtime=0 ) ;---------------------------------------------------------------------------;----------------------------------- ; Find projectile intercept angle from Source (Enemy) to Target (Player) ; Algorithm: Eelco <eelco_hoogendoorn@hotmail.com> ;---------------------------------------------------------------------------; Wrapper: Teasy <thechange@yahoo.com> ; Parameters ; Source: INTER~29.BB ;--------------------------------------------------------------------------------------------------------------- ; (ex,ey) Enemy position ; evx & evy Enemy velocity vector ; (px,py) Player position ; pvx & pvy Player velocity vector ; bs Bullet speed ; maxradius Radius for the player to be in (now or future), 0 = no limit ; maxtime Only shoot if (future) time of impact is below this amount ; (0 = no limit) ;--------------------------------------------------------------------------- ; ;--------------------------------------------------------------------------- ; Make player motion relative to enemy motion ;--------------------------------------------------------------------------- ; es# = Sqr( evxevx + evyevy ) ea# = ATan2( evy,evx ) ; ps# = Sqr( pvxpvx + pvypvy ) pa# = ATan2( pvy,pvx ) ; rpvx#=pvx-evx ; Relative player velocity rpvy#=pvy-evy ; (Cart vector) ; ps=Sqr( rpvxrpvx + rpvyrpvy ) ; Relative player motion (polar) vector pa=ATan2( -rpvy,rpvx ) ; Warning: overrides ps,pa ; ;--------------------------------------------------------------------------- ; Relative distance to player from enemy ;--------------------------------------------------------------------------- ; rx#=px-ex ; Relative player-enemy distance ry#=py-ey ; (Cart vector) ; ;--------------------------------------------------------------------------- ; Player must be moving ;--------------------------------------------------------------------------- ; If Abs( ps )>=0.000001 ; If player speed is more than a little ; : ;----------------------------------------------------------------------- ; Find where player will be, using player motion and bullet speed ;----------------------------------------------------------------------- ; : a#=ATan2( ey-py,ex-px ) ; Angle player->enemy n#=Sin( -pa-a )/bsps ; Angle relative to player, speed scaled ; : ;----------------------------------------------------------------------- ; Player path must be within range for bullet to hit ;----------------------------------------------------------------------- ; : If n>=-1 And n<=1 ; Can bullet ever hit player? ; : ; ;------------------------------------------------------------------- ; New bullet motion for impact ;------------------------------------------------------------------- ; : ; ba#=180+ASin( n )-a ; Rotated angle back to enemy ; : ; bvx#=Cos( ba )bs ; New bullet velocity (cart) vector bvy#=-Sin( ba )bs ; : ; ;------------------------------------------------------------------- ; See when the bullet will impact ;------------------------------------------------------------------- ; : ; d#=bvypvx - bvxpvy ; Intersection ; : ; If Abs( d )>=0.000001 ; Avoid infinitely small t#=( bvxry - bvy*rx )/d ; Time of intersection ; : ; \| If Not ( maxtime>0 And t>=maxtime Or t<0 ) ; Time must be in future but not too far Return VectorAngle( bvx,bvy ) ; Convert back to: Up = 0 degrees EndIf ; : ; \| EndIf ; : ; EndIf EndIf ; Return Math_InterceptAngle_OutOfRange End Function ; Collision Function PointInRect( px,py , rx,ry , w,h ) If px>rx If py>ry If px<rx+w-1 If py<ry+h-1 Return True EndIf EndIf EndIf EndIf End Function --v

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