swwmgz_m/zscript/utility/swwm_utility_math.zsc

// math stuff + gutamatics caching

Struct SWWMProjectionData
{
	swwm_GM_Matrix wtc;
	int viewx, viewy, vieww, viewh;
}

extend Class SWWMUtility
{
	// gutamatics caching
	static void PrepareProjData( out SWWMProjectionData d, Vector3 viewpos, double angle, double pitch, double roll, double fov )
	{
		double aspect = Screen.GetAspectRatio();
		// vertical fov
		double fovratio = (aspect>=1.3)?1.333333:aspect;
		double fovy = 2.*atan(tan(clamp(fov,5,170)/2.)/fovratio);
		// world→clip matrix
		swwm_GM_Matrix view = swwm_GM_Matrix.view(viewpos,angle,pitch,roll);
		swwm_GM_Matrix perp = swwm_GM_Matrix.perspective(fovy,aspect,5,65535);
		d.wtc = perp.multiplyMatrix(view);
		// screen coord data
		int sblocks = CVar.FindCVar('screenblocks').GetInt();
		let [viewx, viewy, vieww, viewh] = Screen.GetViewWindow();
		int sh = Screen.GetHeight();
		int h = sh;
		if ( sblocks < 10 ) h = (sblocks*sh/10)&~7;
		int bottom = sh-(h+viewy-((h-viewh)/2));
		d.viewx = viewx;
		d.viewy = sh-bottom-h;
		d.vieww = vieww;
		d.viewh = h;
	}

	static Vector3 ProjectPoint( SWWMProjectionData d, Vector3 worldpos )
	{
		return d.wtc.multiplyVector3(worldpos).asVector3();
	}

	static Vector2 NDCToViewport( SWWMProjectionData d, Vector3 ndc )
	{
		return (d.viewx,d.viewy)+(((ndc.x+1)*d.vieww)/2,((-ndc.y+1)*d.viewh)/2);
	}

	// checks if a point is inside the viewport
	static bool TestScreenBounds( SWWMProjectionData d, Vector2 vpos )
	{
		return ((vpos.x == clamp(vpos.x,d.viewx,d.viewx+d.vieww))
			&& (vpos.y == clamp(vpos.y,d.viewy,d.viewy+d.viewh)));
	}

	// less code duplication
	static void AdjustClean_1( out double x, out double y )
	{
		x = (x-160)*CleanXFac_1+(Screen.GetWidth()*.5);
		y = (y-100)*CleanYFac_1+(Screen.GetHeight()*.5);
	}
	static void AdjustClean_1x( out double x )
	{
		x = (x-160)*CleanXFac_1+(Screen.GetWidth()*.5);
	}
	static void AdjustClean_1y( out double y )
	{
		y = (y-100)*CleanYFac_1+(Screen.GetHeight()*.5);
	}

	// Vector/Axis utility functions
	static Vector3 Vec3FromAngles( double angle, double pitch )
	{
		return (cos(angle)*cos(pitch),sin(angle)*cos(pitch),-sin(pitch));
	}
	static Vector3 CircleOffset( Vector3 y, Vector3 z, double angle, double radius )
	{
		return y*cos(angle)*radius+z*sin(angle)*radius;
	}
	static Vector3 ConeSpread( Vector3 x, Vector3 y, Vector3 z, double angle, double spread )
	{
		return (x+y*cos(angle)*spread+z*sin(angle)*spread).unit();
	}
	static Vector3 RotateVector3( Vector3 v, double angle )
	{
		Vector2 v2d = Actor.RotateVector(v.xy,angle);
		return (v2d.x,v2d.y,v.z);
	}
	static Vector3 AngleToVector3( double angle, double length = 1. )
	{
		Vector2 v2d = Actor.AngleToVector(angle,length);
		return (v2d.x,v2d.y,0);
	}

	// new GetAxes
	static Vector3, Vector3, Vector3 GetAxes( double angle, double pitch, double roll )
	{
		Quat r = Quat.FromAngles(angle,pitch,roll);
		return r*(1,0,0), r*(0,-1,0), r*(0,0,1);
	}

	// included here until Gutamatics updates to use native quaternions
	static double, double, double ToAngles( Quat q )
	{
		double angle = 0., pitch = 0., roll = 0.;
		double stest = q.z*q.x-q.w*q.y;
		double angY = 2.*(q.w*q.z+q.x*q.y);
		double angX = 1.-2.*(q.y*q.y+q.z*q.z);
		if ( stest < -.4999995 )
		{
			angle = atan2(angY,angX);
			pitch = 90.;
			roll = swwm_GM_GlobalMaths.Normalize180(angle+(2.*atan2(q.x,q.w)));
		}
		else if ( stest > .4999995 )
		{
			angle = atan2(angY,angX);
			pitch = -90.;
			roll = swwm_GM_GlobalMaths.Normalize180(angle+(2.*atan2(q.x,q.w)));
		}
		else
		{
			angle = atan2(angY,angX);
			pitch = -asin(2.*stest);
			roll = atan2(2.*(q.w*q.x+q.y*q.z),1.-2.*(q.x*q.x+q.y*q.y));
		}
		return angle, pitch, roll;
	}

	// for aiming and shooting
	static Vector3 GetPlayerViewDir( Actor player )
	{
		Quat r = Quat.FromAngles(player.angle+player.viewangle,player.pitch+player.viewpitch,player.roll+player.viewroll);
		return r*(1,0,0);
	}
	static play Vector3 GetPlayerAimDir( Actor player )
	{
		FTranslatedLineTarget t;
		double pitch = player.BulletSlope(t);
		Quat r;
		if ( !t.linetarget ) r = Quat.FromAngles(player.angle+player.viewangle,player.pitch+player.viewpitch,player.roll+player.viewroll);
		else r = Quat.FromAngles(player.angle+player.viewangle,pitch,player.roll+player.viewroll);
		return r*(1,0,0);
	}
	static Vector3, Vector3, Vector3 GetPlayerAxes( Actor player )
	{
		Quat r = Quat.FromAngles(player.angle+player.viewangle,player.pitch+player.viewpitch,player.roll+player.viewroll);
		return r*(1,0,0), r*(0,-1,0), r*(0,0,1);
	}
	static play Vector3, Vector3, Vector3 GetPlayerAxesAutoAimed( Actor player )
	{
		FTranslatedLineTarget t;
		double pitch = player.BulletSlope(t);
		Quat r;
		if ( !t.linetarget ) r = Quat.FromAngles(player.angle+player.viewangle,player.pitch+player.viewpitch,player.roll+player.viewroll);
		else r = Quat.FromAngles(player.angle+player.viewangle,pitch,player.roll+player.viewroll);
		return r*(1,0,0), r*(0,-1,0), r*(0,0,1);
	}
	static Vector3 GetPlayerEye( Actor player )
	{
		if ( !player.viewpos )
			return player.Vec2OffsetZ(0,0,player.player.viewz);
		if ( player.viewpos.flags&VPSF_ABSOLUTEPOS )
			return player.viewpos.offset;
		Vector3 origin = player.Vec2OffsetZ(0,0,player.player.viewz);
		if ( player.viewpos.flags&VPSF_ABSOLUTEOFFSET )
			return level.Vec3Offset(origin,player.viewpos.offset);
		Quat r = Quat.FromAngles(player.angle,player.pitch,player.roll); // viewangles are not used
		return level.Vec3Offset(origin,r*player.viewpos.offset);
	}
	static Vector3 GetFireOffset( Actor player, double x, double y, double z )
	{
		Vector3 origin = GetPlayerEye(player);
		Quat r = Quat.FromAngles(player.angle+player.viewangle,player.pitch+player.viewpitch,player.roll+player.viewroll);
		return level.Vec3Offset(origin,r*(x,-y,z));
	}

	// thanks zscript
	static double fract( double a )
	{
		return a-floor(a);
	}

	static double lerp( double a, double b, double theta )
	{
		return a*(1.-theta)+b*theta;
	}
	static Vector3 LerpVector3( Vector3 a, Vector3 b, double theta )
	{
		return a*(1.-theta)+b*theta;
	}
	static Vector2 LerpVector2( Vector2 a, Vector2 b, double theta )
	{
		return a*(1.-theta)+b*theta;
	}
	static Color LerpColor( Color a, Color b, double theta )
	{
		Color c = Color(
			int(a.a*(1.-theta)+b.a*theta),
			int(a.r*(1.-theta)+b.r*theta),
			int(a.g*(1.-theta)+b.g*theta),
			int(a.b*(1.-theta)+b.b*theta)
		);
		return c;
	}

	static double MapRange( double amin, double amax, double bmin, double bmax, double theta )
	{
		return bmin+(theta-amin)*(bmax-bmin)/(amax-amin);
	}

	// this can probably be simplified, but I'm lazy
	static Vector3 HSVtoRGB( Vector3 hsv )
	{
		Vector3 p;
		p.x = abs(fract(hsv.x+1.)*6.-3.);
		p.y = abs(fract(hsv.x+(2./3.))*6.-3.);
		p.z = abs(fract(hsv.x+(1./3.))*6.-3.);
		Vector3 p2;
		p2.x = (1.-hsv.y)+clamp(p.x-1.,0.,1.)*hsv.y;
		p2.y = (1.-hsv.y)+clamp(p.y-1.,0.,1.)*hsv.y;
		p2.z = (1.-hsv.y)+clamp(p.z-1.,0.,1.)*hsv.y;
		return p2*hsv.z;
	}

	// "fast" exponentiation with integer exponents using loops
	static double IntPowF( double base, int exp )
	{
		if ( exp < 0 ) return 1./IntPowF(base,-exp);
		if ( exp == 0 ) return 1.;
		double rslt = base;
		for ( int i=0; i<exp; i++ ) rslt *= base;
		return rslt;
	}
	static int IntPow( int base, int exp )
	{
		if ( exp < 0 ) return int(1./IntPow(base,-exp));
		if ( exp == 0 ) return 1;
		int rslt = base;
		for ( int i=0; i<exp; i++ ) rslt *= base;
		return rslt;
	}

	// pitch from one actor's eyes to another based on a specific fraction of its height
	// meant for player view, Actor.PitchTo is recommended for more "general" situations
	static double PitchTo( Actor a, Actor b, double hfact = 1. )
	{
		if ( !a || !b ) return 0;
		Vector3 thispos = a.player?a.Vec2OffsetZ(0,0,a.player.viewz):a.Vec3Offset(0,0,a.GetCameraHeight()-a.floorclip);
		Vector3 otherpos = b.Vec3Offset(0,0,b.height*hfact);
		Vector3 diff = level.Vec3Diff(thispos,otherpos);
		return -atan2(diff.z,diff.xy.length());
	}

	// box intersection check, for collision detection
	static bool BoxIntersect( Actor a, Actor b, Vector3 ofs = (0,0,0), int pad = 0 )
	{
		Vector3 diff = level.Vec3Diff(level.Vec3Offset(a.pos,ofs),b.pos);
		if ( (abs(diff.x) > (a.radius+b.radius+pad)) || (abs(diff.y) > (a.radius+b.radius+pad)) ) return false;
		if ( (diff.z > a.height+pad) || (diff.z < -(b.height+pad)) ) return false;
		return true;
	}

	// extruded box intersection check, useful when checking things that might be hit along a path
	static bool ExtrudeIntersect( Actor a, Actor b, Vector3 range, int steps, int pad = 0 )
	{
		if ( steps <= 0 ) return BoxIntersect(a,b,pad:pad);
		double step = 1./steps;
		for ( double i=step; i<=1.; i+=step )
		{
			if ( BoxIntersect(a,b,range*i,pad) )
				return true;
		}
		return false;
	}

	// sphere intersection check, useful for proximity detection
	static bool SphereIntersect( Actor a, Vector3 p, double radius )
	{
		Vector3 ap = p+level.Vec3Diff(p,a.pos);	// portal-relative actor position
		Vector3 amin = ap+(-a.radius,-a.radius,0),
			amax = ap+(a.radius,a.radius,a.height);
		double distsq = 0.;
		if ( p.x < amin.x ) distsq += (amin.x-p.x)*(amin.x-p.x);
		if ( p.x > amax.x ) distsq += (p.x-amax.x)*(p.x-amax.x);
		if ( p.y < amin.y ) distsq += (amin.y-p.y)*(amin.y-p.y);
		if ( p.y > amax.y ) distsq += (p.y-amax.y)*(p.y-amax.y);
		if ( p.z < amin.z ) distsq += (amin.z-p.z)*(amin.z-p.z);
		if ( p.z > amax.z ) distsq += (p.z-amax.z)*(p.z-amax.z);
		return (distsq <= (radius*radius));
	}

	// hitscan exit point calculation given actor, entry point and direction
	static Vector3 TraceExit( Actor a, Vector3 p, Vector3 d )
	{
		Vector3 ap = p+level.Vec3Diff(p,a.pos);	// portal-relative actor position
		Vector3 amin = ap+(-a.radius,-a.radius,0),
			amax = ap+(a.radius,a.radius,a.height);
		Vector3 tmax, div = (1./d.x,1./d.y,1./d.z);
		if ( div.x < 0 ) tmax.x = (amin.x-p.x)*div.x;
		else tmax.x = (amax.x-p.x)*div.x;
		if ( div.y < 0 ) tmax.y = (amin.y-p.y)*div.y;
		else tmax.y = (amax.y-p.y)*div.y;
		if ( div.z < 0 ) tmax.z = (amin.z-p.z)*div.z;
		else tmax.z = (amax.z-p.z)*div.z;
		return level.Vec3Offset(p,min(min(tmax.x,tmax.y),tmax.z)*d);
	}

	// Liang-Barsky line clipping
	static bool, Vector2, Vector2 LiangBarsky( Vector2 minclip, Vector2 maxclip, Vector2 v0, Vector2 v1 )
	{
		double t0 = 0., t1 = 1.;
		double xdelta = v1.x-v0.x;
		double ydelta = v1.y-v0.y;
		double p, q, r;
		for ( int i=0;i<4; i++ )
		{
			switch ( i )
			{
			case 0:
				p = -xdelta;
				q = -(minclip.x-v0.x);
				break;
			case 1:
				p = xdelta;
				q = (maxclip.x-v0.x);
				break;
			case 2:
				p = -ydelta;
				q = -(minclip.y-v0.y);
				break;
			case 3:
				p = ydelta;
				q = (maxclip.y-v0.y);
				break;
			}
			if ( (p == 0.) && (q<0.) ) return false, (0,0), (0,0);
			if ( p < 0 )
			{
				r = q/p;
				if ( r > t1 ) return false, (0,0), (0,0);
				else if ( r > t0 ) t0 = r;
			}
			else if ( p > 0 )
			{
				r = q/p;
				if ( r < t0 ) return false, (0,0), (0,0);
				else if ( r < t1 ) t1 = r;
			}
		}
		Vector2 ov0 = v0+(xdelta,ydelta)*t0;
		Vector2 ov1 = v0+(xdelta,ydelta)*t1;
		return true, ov0, ov1;
	}

	static play bool InPlayerFOV( PlayerInfo p, Actor a, double maxdist = 0. )
	{
		double vfov = p.fov*.5;
		double hfov = atan(Screen.GetAspectRatio()*tan(vfov));
		let mo = p.camera;
		if ( !mo ) return false;
		Vector3 pp;
		if ( !a.CheckSight(mo,SF_IGNOREVISIBILITY|SF_IGNOREWATERBOUNDARY) ) return false;
		if ( mo is 'PlayerPawn' ) pp = mo.Vec2OffsetZ(0,0,PlayerPawn(mo).player.viewz);
		else pp = mo.Vec3Offset(0,0,mo.GetCameraHeight());
		Vector3 sc = level.SphericalCoords(pp,a.pos,(mo.angle,mo.pitch));
		if ( (abs(sc.x) > hfov) || (abs(sc.y) > vfov) ) return false;
		if ( (maxdist > 0.) && (sc.z > maxdist) ) return false;
		return true;
	}

	// ui-friendly version without CheckSight call
	static bool InPlayerFOVSimple( PlayerInfo p, Actor a, double maxdist = 0. )
	{
		double vfov = p.fov*.5;
		double hfov = atan(Screen.GetAspectRatio()*tan(vfov));
		let mo = p.camera;
		if ( !mo ) return false;
		Vector3 pp;
		if ( mo is 'PlayerPawn' ) pp = mo.Vec2OffsetZ(0,0,PlayerPawn(mo).player.viewz);
		else pp = mo.Vec3Offset(0,0,mo.GetCameraHeight());
		Vector3 sc = level.SphericalCoords(pp,a.pos,(mo.angle,mo.pitch));
		if ( (abs(sc.x) > hfov) || (abs(sc.y) > vfov) ) return false;
		if ( (maxdist > 0.) && (sc.z > maxdist) ) return false;
		return true;
	}

	// calculate angle, pitch and yscale of YBeam based on direction vector and length
	static double, double, double CalcYBeam( Vector3 dir, double dist )
	{
		if ( level.pixelstretch == 1. )
		{
			// ez modo
			double angle = atan2(dir.y,dir.x);
			double pitch = asin(-dir.z)+90;
			return angle, pitch, dist;
		}
		dir.z *= level.pixelstretch;
		double len = dir.length();
		dir /= len;
		double angle = atan2(dir.y,dir.x);
		double pitch = asin(-dir.z)+90;
		double yscale = dist*len;
		return angle, pitch, yscale;
	}
}