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}GBYɫSrsY.CԻ/9"1n4SN`J_-E ok7P\b[;m`?7t,ݨ9Xs5pY TXn+k:c3.+LQZr{2 %7Ȑ6" Gg0k*kH1Yb1$dI77fa:E˼w c 6I&do24O x{PTU0C.LEtx- [acL`Y+!̸0`ZRMʄ4Y1 K) ٖYw{w  q` קb1'N8qĉtFdI/S&:1BQI2>ĩl+g_ 7Wtz!Md1C.*RBTTyyTlI<s@00ѡR)_&zxxntwWL^A٤ I6fsة09PG)¹nэ0%Ĵ% h:Rz^p1xдbDyY%&$n XnU%ߐ.RAabԨs@V"qRv^w`ԃ5Lb,B:Z~Tip.((D^g>rHԫbjK<8x.:P-w&8`bc$`A=yQ0YJ|C.ٹ ~:ފ(z xugH9jI,8Eo!gWgD3EoF.!GJOJr fTH|B@4~w鯣ϵ#:"Zu\[7v`tE1s߀Eg}~9Ѽ; 1H螑>\,8j?mˀ]v>?qw3TuaEt{7G!F@"~WBX8gnD%!h;:n0+VZs8ݧ<(js~x_bL߸eլEyƐ2YmgYioq*t J23ƈΔV k翅Ej, ^sUp'`gqgs֗Y<7o"_H۬֜Ìi`~2 c(Zϧ.=.q^d)@ !vxn}U\bPV??X Tu ~v-l4]3Q0ml V_p.#Gb;= <$g 3Q5F|[P&Rt$-Cз-5Ms# NJcLWUT‚â{`eg.=7a[M@TB ִRv%-=)Z1204wZF4W&l+g`# #=nBF"aN"m%7ai oAGb(pbY`lx4pxxrG"P(BՁr8 8h h*TO$\#~q2 AT}ջvlN{<_^W,Fd)ˠñx/67ˀPAVH@h5g;vE4 c(KK66SK%;#na{|4߱KJfX_]e.>.]iLSZFTjV4U[W$ɋtœ0C`o%WYfS~9? 2)yܜTP(X6?<ȎۣU6 02H9n,ZOS;;B#8[3n$t)% 58<Ԋ)jqiH(Ws ]P7GƮͣ(%vxG9s[Di?Bxr|c7`UOM #~D}.O+<߾'@G}>y?Rٲsprite1 ,xsf@P ?48@ )r16sprite2   Qxs5a3 b(fdH@Q@(EhtDR/.0F42d8, OE1cꆏQ4Fasprite0  Zxs-cd3 b.(fd;@Q@ 10MP."πԀBK-E30lWd/ϰ _Kmwall-ew #xsf@@Č ` X@Fq"wall-ns %xsf@,@,Č ` aH#Bpath0`gY@T eY@8@eY@_@hY@W@GY@``@_@Y@@T@]@Y@@Q@e@Y@@e@Y@ @U@Y@P@\@Y@@[]@Y@@U0Y@@`VY@ `\Y@path1Y@0Y@TY@@@TY@T@TY@X@TY@X@dY@object0 -action_set_alarm 2*pi/.0150000000c alpharadians0000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game00000000c alpharadians.015000000daction_if_variable alpharadians2*pi200000c alpharadiansalpharadians-2*pi000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000  action_color 016777215000000 action_draw_fontArial,8,16776960,0,0,0,010000000[Lroom_caption = "angle degrees "+string(alpharadians*180/pi)+" sine "+ string(sin(alpharadians)) +" cosine " +string(cos(alpharadians)) draw_circle(320,240,200) draw_line(320,0,320,480) draw_line(0,240,640,240) draw_line(320,240,320+200*cos(alpharadians),240-200*sin(alpharadians)) draw_line(320+200*cos(alpharadians),240, 320+200*cos(alpharadians),240-200*sin(alpharadians)) pen_color= c_aqua draw_arc(320-20,240-20,320+20,240+20,320+20,240, 320 +20*cos(alpharadians),240-20*sin(alpharadians)) draw_text(320+20,240-20,string(alpharadians*180/pi)+" degrees") pen_color= c_white0000000 sineobject  action_draw_fontArial,8,16777215,0,0,0,010000000[draw_text(320 +200*cos(object0.alpharadians), 240 -100*sin(object0.alpharadians),"sine="+ string(sin(object0.alpharadians))) 0000000 cosobject  action_draw_fontArial,8,16777215,0,0,0,010000000[ddraw_text(280 +100*cos(object0.alpharadians), 260,"cosine="+ string(cos(object0.alpharadians))) 0000000whatis -action_set_alarm500000000ctextline0000000[ pen_size=1 0000000-action_set_alarm900000000ctextline0.5000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game000000000  action_color 016777215000000 action_draw_fontArial,14,65535,1,0,0,010000000action_draw_textWhat is trigonometry?20000000 action_draw_fontArial,12,65535,0,0,0,010000000 action_if textline>00000000action_draw_textIt relates angles to x and y204000000 action_if textline>10000000action_draw_text/Draw a right angled triangle between two points208000000 action_if textline>2000000000000000action_draw_text*The diagonal line is called the hypotenuse2012000000 action_draw_fontArial,8,16777215,0,0,0,010000000action_draw_texthypotenuse (r)46012000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_line42024062040000000000000 action_if textline>3000000000000000action_draw_text,The length of the line opposite to the angle2016000000action_draw_text%divided by the hypotenuse is the sine2018000000 action_draw_fontArial,8,16777215,0,0,0,010000000action_draw_text opposite (y)54018000000action_draw_textangle45022000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_line620240620400000[Mdraw_arc(420-20,240-20,420+20,240+20,420+20,240, 420 +20*0.707,240-20*0.707)000000000000000 action_if textline>40000000action_draw_text sin(angle) =y/r2020000000 action_if textline>5000000000000000action_draw_text'The length of the line beside the angle2024000000action_draw_text4divided by the hypotenuse is the cosine of the angle2026000000 action_draw_fontArial,8,16777215,0,0,0,010000000action_draw_text adjacent (x)48024000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_line420240620240000000000000 action_if textline>60000000action_draw_text cos(angle)= x/r2028000000 action_if textline>70000000action_draw_text1And the tangent is the opposite over the adjacent2032000000 action_if textline>80000000action_draw_text tan(angle) = y/x2034000000 action_if textline>90000000action_draw_textwatch...2038000000 action_if textline>9.50000000action_next_room00000000 tanobject  action_draw_fontArial,14,16777215,0,0,0,010000000action_draw_text*"tan= "+string(tan (object0.alpharadians))505000000 objectarsin -action_set_alarm500000000ctextline0000000-action_set_alarm1200000000ctextline1000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000  action_color 016777215000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_text1The opposite functions are arsin, arcos and artan20000000 action_if textline>00000000action_draw_text7That's when you know any two of x, y and the hypotenuse204000000 action_if textline>10000000action_draw_textand want to work out the angle208000000 action_if textline>20000000action_draw_text For example, if you know x and y2012000000 action_if textline>30000000action_draw_textthe angle is artan y/x2016000000 action_if textline>40000000action_draw_text"but always check that x isn't zero2020000000 action_if textline>50000000action_draw_textor you get an error2024000000 action_if textline>60000000action_change_object 71000000 objectradian -action_set_alarm500000000ctextline0000000-action_set_alarm1200000000ctextline1000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000  action_color 016777215000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_text,Angles can be measured in degrees or radians20000000 action_if textline>00000000action_draw_text&There are 360 degrees in a full circle204000000 action_if textline>1000000000000000action_draw_text:one radian is when the length of the arc equals the radius208000000 action_draw_fontArial,8,16777215,0,0,0,010000000action_draw_text138025000000action_draw_text143019000000action_draw_text1 radian34022000000 action_draw_fontArial,12,65535,0,0,0,010000000[draw_arc(320-100,240-100,320+100,240+100,320+100,240, 320 +100*cos(1),240-100*sin(1)) draw_arc(320-20,240-20,320+20,240+20,320+20,240, 320 +20*cos(1),240-20*sin(1)) draw_line(320,240,420,240) draw_line(320,240,320 +100*cos(1),240-100*sin(1))000000000000000 action_if textline>20000000action_draw_text'the circumference of a circle is 2 * pi2012000000 action_if textline>30000000action_draw_text'so there are 2 * pi radians in a circle2016000000 action_if textline>40000000action_draw_textTo convert degrees to radians,2020000000 action_if textline>50000000action_draw_textmultiply by 2*pi/3602024000000 action_if textline>60000000action_change_object 81000000whatuse -action_set_alarm500000000ctextline0000000-action_set_alarm1200000000ctextline1000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000  action_color 016777215000000 action_draw_fontArial,12,65535,0,0,0,010000000action_draw_textWhat use is all this?20000000 action_if textline>00000000action_draw_textYou can use this for...204000000 action_if textline>10000000action_draw_texta clock208000000 action_if textline>20000000action_draw_textan aiming sight2012000000 action_if textline>30000000action_draw_textto always face an object2016000000 action_if textline>40000000action_draw_text 3D graphics2020000000 action_if textline>5000000000000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game0000000000000000object0 -action_set_alarm1200000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game00000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000[_pen_size=2 draw_circle(200,200,130) x2=200+100*sin(2*pi*current_second/60) y2=200-100*cos(2*pi*current_second/60) draw_line(200,200,x2,y2) pen_size=4 x2=200+100*sin(2*pi*current_minute/60) y2=200-100*cos(2*pi*current_minute/60) draw_line(200,200,x2,y2) pen_size=6 x2=200+50*sin(2*pi*(current_hour+current_minute/60)/12) y2=200-50*cos(2*pi*(current_hour+current_minute/60)/12) draw_line(200,200,x2,y2) for(i=0; i<12; i+=1) { x1=200+110*sin(2*pi*(i)/12) y1=200-110*cos(2*pi*(i)/12) x2=200+125*sin(2*pi*(i)/12) y2=200-125*cos(2*pi*(i)/12) draw_line(x1,y1,x2,y2) } 0000000shooter -action_set_alarm2500000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game00000000cfacing+90+180/pi*arctan((x-target.x)/(y-target.y))000000 action_if y-target.y<00000000cfacing180000000c image_single facing/10000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000target w action_path05000000car action_create_object 140000000c sightangle0000000-action_set_alarm500000000-action_set_alarm100000000action_create_object 150000000 c sightangle.01000000csight.xx+30*cos(sightangle)000000csight.yy-30*sin(sightangle)000000 action_if sightangle>pi000000000000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game0000000000000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000sight bullet iaction_move_pointsight.xsight.y1000000kaction_set_gravity2700.5000000viewport [ pen_size=1 0000000cfacing0000000]viewer facing north0000000czed480-y000000cexx-320000000w action_path22000000c room_captionH"direction: "+string(facing) +" x: " +string(x) +" y: " +string(y) 000000cexx-320000000czed480-y000000cfacing -direction+90000000action_if_next_room00000000action_next_room0000000000000000Laction_end_game00000000action_if_next_room00000000action_next_room0000000000000000Kaction_restart_game00000000]disable the draw event0000000wallew   action_color 652800000000[ex1=x-320 ex2=ex1+sprite_width zed1=480-y zed2=480-y // //distance to point 1&2 distto1=sqrt(sqr(viewport.ex-ex1)+sqr(viewport.zed-zed1)) distto2=sqrt(sqr(viewport.ex-ex2)+sqr(viewport.zed-zed2)) // //get depth order depth=distto1 if distto1>distto2 depth=distto2 // //angle to point 1&2 if(zed1-viewport.zed!=0) angleto1=(180/pi)*arctan((ex1-viewport.ex)/(zed1-viewport.zed)) else { if(ex1-viewport.ex>0)angleto1=90 else angleto1=-90 } if(zed2-viewport.zed!=0) angleto2=(180/pi)*arctan((ex2-viewport.ex)/(zed2-viewport.zed)) else { if(ex2-viewport.ex>0)angleto2=90 else angleto2=-90 } if(zed1-viewport.zed<0) angleto1+=180 //arctan function is only 2 quadrant if(zed2-viewport.zed<0) angleto2+=180 //arctan function is only 2 quadrant // angleto1=angleto1-viewport.facing angleto2=angleto2-viewport.facing if angleto1<-180 angleto1+=360 if angleto2<-180 angleto2+=360 if angleto1>180 angleto1-=360 if angleto2>180 angleto2-=360 //check either points are in front if((angleto1>-90&&angleto1<90)||(angleto2>-90&&angleto2<90)) { draw_polygon_begin() //Start describing a polygon for drawing. draw_polygon_vertex(320+angleto1*10,240-5000/distto1) //Add vertex1 bottom draw_polygon_vertex(320+angleto1*10,240+5000/distto1) //Add vertex1 top draw_polygon_vertex(320+angleto2*10,240+5000/distto2) //Add vertex2 top draw_polygon_vertex(320+angleto2*10,240-5000/distto2) //Add vertex2 bottom draw_polygon_end() //End the description of the polygon. This function actually draws it }0000000wallns    action_color 83888630000000[ex1=x-320 ex2=x-320 zed1=480-y zed2=480-y-sprite_height // //distance to point 1&2 distto1=sqrt(sqr(viewport.ex-ex1)+sqr(viewport.zed-zed1)) distto2=sqrt(sqr(viewport.ex-ex2)+sqr(viewport.zed-zed2)) // //get depth order depth=distto1 if distto1>distto2 depth=distto2 // //angle to point 1&2 if(zed1-viewport.zed!=0) angleto1=(180/pi)*arctan((ex1-viewport.ex)/(zed1-viewport.zed)) else { if(ex1-viewport.ex>0)angleto1=90 else angleto1=-90 } if(zed2-viewport.zed!=0) angleto2=(180/pi)*arctan((ex2-viewport.ex)/(zed2-viewport.zed)) else { if(ex2-viewport.ex>0)angleto2=90 else angleto2=-90 } if(zed1-viewport.zed<0) angleto1+=180 //arctan function is only 2 quadrant if(zed2-viewport.zed<0) angleto2+=180 //arctan function is only 2 quadrant angleto1=angleto1-viewport.facing angleto2=angleto2-viewport.facing if angleto1<-180 angleto1+=360 if angleto2<-180 angleto2+=360 if angleto1>180 angleto1-=360 if angleto2>180 angleto2-=360 //check either points are in front if((angleto1>-90&&angleto1<90)||(angleto2>-90&&angleto2<90)) { draw_polygon_begin() //Start describing a polygon for drawing. draw_polygon_vertex(320+angleto1*10,240-5000/distto1) //Add vertex1 bottom draw_polygon_vertex(320+angleto1*10,240+5000/distto1) //Add vertex1 top draw_polygon_vertex(320+angleto2*10,240+5000/distto2) //Add vertex2 top draw_polygon_vertex(320+angleto2*10,240-5000/distto2) //Add vertex2 bottom draw_polygon_end() //End the description of the polygon. This function actually draws it }0000000roomsin        `roomcos        ` roomintro        roomtan        p@ roomarsin        room0         room0         0P room0        ` room1        *@pppP0@P@0@@ @@†@`Æ@Ć`ņƆdžȆɆ@ʆ0ˆ ̆͆ΆφІ@`цP`҆``ӆp`Ԇ`Ն`ֆX׆P؆@ن0چ ۆ܆ ݆ކ߆r{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset1 Courier New;}{\f3\fmodern\fcharset1 Courier New;}{\f4\fswiss\fcharset1 Arial;}{\f5\fswiss\fcharset1 Arial;}{\f6\fmodern Courier New;}{\f7\fswiss Arial;}} {\colortbl\red0\green0\blue0;\red0\green128\blue0;\red128\green0\blue0;\red0\green0\blue255;\red0\green0\blue128;\red128\green0\blue128;} \deflang1033\pard\plain\f5\fs24\cf0\b A demonstration of trigonometric functions and their uses\plain\f5\fs24\cf0 \par Tony Forster 21/7/04 \par May be copied with acknowlegement of authorship \par \par \plain\f5\fs24\cf0\b Animated graphs \par \plain\f5\fs24\cf0 I have chosen to use normal cartesian graphing coordinates, y is up. The angle starts from the x axis so right is zero degrees. Note that Gamemaker uses the convention of y being down and angle zero degrees being to the left, this means that minus signs pop up unexpectedly in formulae. \par \par \plain\f5\fs24\cf0\b Clock \par \plain\f5\fs24\cf0 See the code in the draw event: \par \par \plain\f3\fs20\cf3 pen_size\plain\f3\fs20\cf0 =2\plain\f3\fs20 \par \plain\f3\fs20\cf1 // draw the circle \par \plain\f3\fs20\cf4 draw_circle\plain\f3\fs20\cf0 (200,200,130) \plain\f3\fs20 \par \plain\f3\fs20\cf1 // draw the second hand \par \plain\f3\fs20\cf0 x2=200+100*\plain\f3\fs20\cf4 sin\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *\plain\f3\fs20\cf3 current_second\plain\f3\fs20\cf0 /60) \plain\f3\fs20 \par \plain\f3\fs20\cf0 y2=200-100*\plain\f3\fs20\cf4 cos\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *\plain\f3\fs20\cf3 current_second\plain\f3\fs20\cf0 /60)\plain\f3\fs20 \par \plain\f3\fs20\cf4 draw_line\plain\f3\fs20\cf0 (200,200,x2,y2) \plain\f3\fs20 \par \plain\f3\fs20\cf1 // draw the minute hand \par \plain\f3\fs20\cf3 pen_size\plain\f3\fs20\cf0 =4\plain\f3\fs20 \par \plain\f3\fs20\cf0 x2=200+100*\plain\f3\fs20\cf4 sin\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *\plain\f3\fs20\cf3 current_minute\plain\f3\fs20\cf0 /60) \plain\f3\fs20 \par \plain\f3\fs20\cf0 y2=200-100*\plain\f3\fs20\cf4 cos\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *\plain\f3\fs20\cf3 current_minute\plain\f3\fs20\cf0 /60)\plain\f3\fs20 \par \plain\f3\fs20\cf4 draw_line\plain\f3\fs20\cf0 (200,200,x2,y2) \plain\f3\fs20 \par \plain\f3\fs20\cf1 // draw the hour hand \par \plain\f3\fs20\cf3 pen_size\plain\f3\fs20\cf0 =6\plain\f3\fs20 \par \plain\f3\fs20\cf0 x2=200+50*\plain\f3\fs20\cf4 sin\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(\plain\f3\fs20\cf3 current_hour\plain\f3\fs20\cf0 +\plain\f3\fs20\cf3 current_minute\plain\f3\fs20\cf0 /60)/12) \plain\f3\fs20 \par \plain\f3\fs20\cf0 y2=200-50*\plain\f3\fs20\cf4 cos\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(\plain\f3\fs20\cf3 current_hour\plain\f3\fs20\cf0 +\plain\f3\fs20\cf3 current_minute\plain\f3\fs20\cf0 /60)/12)\plain\f3\fs20 \par \plain\f3\fs20\cf4 draw_line\plain\f3\fs20\cf0 (200,200,x2,y2) \plain\f3\fs20 \par \plain\f3\fs20\cf1 // draw the face markings \par \plain\f3\fs20\cf0\b for\plain\f3\fs20\cf0 (i=0; i<12; i+=1)\plain\f3\fs20 \par \plain\f3\fs20\cf0\b \{\plain\f3\fs20 \par \plain\f3\fs20\cf0 x1=200+110*\plain\f3\fs20\cf4 sin\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(i)/12) \plain\f3\fs20 \par \plain\f3\fs20\cf0 y1=200-110*\plain\f3\fs20\cf4 cos\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(i)/12)\plain\f3\fs20 \par \plain\f3\fs20\cf0 x2=200+125*\plain\f3\fs20\cf4 sin\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(i)/12) \plain\f3\fs20 \par \plain\f3\fs20\cf0 y2=200-125*\plain\f3\fs20\cf4 cos\plain\f3\fs20\cf0 (2*\plain\f3\fs20\cf2 pi\plain\f3\fs20\cf0 *(i)/12)\plain\f3\fs20 \par \plain\f3\fs20\cf0 \plain\f3\fs20\cf4 draw_line\plain\f3\fs20\cf0 (x1,y1,x2,y2) \plain\f3\fs20 \par \plain\f3\fs20\cf0\b \}\plain\f3\fs20 \par \par \plain\f5\fs24\cf0 \par \plain\f5\fs24\cf0\b Rotate \par \plain\f7\fs24\cf0 Uses trigonometric functions to make a sprite always face another object \par \par \plain\f5\fs24\cf0 See asteroids.gmd from resource pack3 at www.gamemaker.nl to see how to use the angle to select an image from a multi-image sprite. \par \par This is a little more difficult, we have to first calculate the angle to our target. \par \par The angle is \plain\f3\fs20\cf0 90+180/pi*arctan((x-target.x)/(y-target.y)) \par \plain\f7\fs24\cf0 \par This angle is in radians not degrees so multiply by 180/pi \par 180/pi*arctan returns a value between -90 and 90 so add 90 to get a positive number \plain\f5\fs24\cf0 and because arctan is only 2 quadrant, we need: \par \plain\f3\fs20\cf0 if y-target.y<0 then facing = +180 relative\plain\f5\fs24\cf0 \par \par A simpler way is to move towards the target at speed zero, that sets the direction which can be used to select the image.\plain\f7\fs24\cf0 \par \par \plain\f5\fs24\cf0\b Gunsight \par \plain\f5\fs24\cf0 A gunsight with a circular path \par \par To get a gunsight to move in a circle, radius 30 around a point x,y \par \plain\f3\fs20\cf0 sight.x = x+30*cos(sightangle) \par sight.y = y+30*sin(sightangle) \par \plain\f5\fs24\cf0 \par \plain\f7\fs24\cf0\b 3D \par \plain\f7\fs24\cf0 With true perspective, 3D games show parallel lines converging at infinity. A rectangular wall looks rectangular straight on and a trapezium if viewed obliquely. \par \par Coordinates ex and zed are used. Zed is north and ex is east. \par \par There is the viewport object which moves around but has no draw event. There are 2 kinds of wall object \par \par Any wall will have coordinates ex1,zed1 ex2,zed2. The distance to the viewer and angle are computed. \par \par \plain\f6\fs20\cf0 distto1=\plain\f6\fs20\cf4 sqrt\plain\f6\fs20\cf0 (\plain\f6\fs20\cf4 sqr\plain\f6\fs20\cf0 (\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .ex-ex1)+\plain\f6\fs20\cf4 sqr\plain\f6\fs20\cf0 (\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .zed-zed1)) \par distto2=\plain\f6\fs20\cf4 sqrt\plain\f6\fs20\cf0 (\plain\f6\fs20\cf4 sqr\plain\f6\fs20\cf0 (\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .ex-ex2)+\plain\f6\fs20\cf4 sqr\plain\f6\fs20\cf0 (\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .zed-zed2)) \par \plain\f7\fs24\cf0 \par \plain\f6\fs20\cf0 angleto1=(180/\plain\f6\fs20\cf2 pi\plain\f6\fs20\cf0 )*\plain\f6\fs20\cf4 arctan\plain\f6\fs20\cf0 ((ex1-\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .ex)/(zed1-\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .zed)) \par angleto2=(180/\plain\f6\fs20\cf2 pi\plain\f6\fs20\cf0 )*\plain\f6\fs20\cf4 arctan\plain\f6\fs20\cf0 ((ex2-\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .ex)/(zed2-\plain\f6\fs20\cf5 viewport\plain\f6\fs20\cf0 .zed)) \par \plain\f7\fs24\cf0 \par Walls are drawn as polygons, the screen x is proportional to the angle and the screen height inversely proportional to the distance. This mostly works unless you stand too close to a wall edge. Problems can be minimised by keeping away from walls and keeping wall segments short. \par \par \plain\f6\fs20\cf0 draw_polygon_vertex(320+angleto1*10,240-5000/distto1) \par \par \plain\f7\fs24\cf0 Dont draw walls that are behind you. The formula below can occasionally flash up walls that are behind you, replacing the or (||) with an and (&&) gives the opposite problem, walls in front dissapearing. Problems are minimised by keeping away from walls and keeping wall segments short. \par \par \plain\f6\fs20\cf0 (angleto1>-90&&angleto1<90)||(angleto2>-90&&angleto2<90) \par \par \plain\f7\fs24\cf0 Near walls must obscure far ones so the depth of each wall is taken as the distance of the nearer edge. \par \par \plain\f6\fs20\cf3 depth\plain\f6\fs20\cf0 =distto1 \par \plain\f6\fs20\cf0\b if\plain\f6\fs20\cf0 distto1>distto2 \plain\f6\fs20\cf3 depth\plain\f6\fs20\cf0 =distto2 \par \plain\f7\fs24\cf0 \par \par \plain\f5\fs24\cf0 \par }    SpritesROTATEsprite0ROTATEsprite0sprite2gunsightsprite0sprite1sprite23Dsprite0wall-ew wall-nsSounds BackgroundsPathsROTATEpath03Dpath1Scripts Data Files Time LinesObjects object0 sineobject cosobjectwhatis tanobject objectarsin objectradianwhatuse clock object0 ROTATE shooter target gunsight carsightbullet3DwallewwallnsviewportRooms  roomintroroomsinroomcosroomtan roomarsinclockroom0 ROTATE room0 gunsight room0 3D room1 Game Information Game Options