document body style minHeight 200px let status document createElement div status innerHTML Lines document body appendChild status let ww window innerWidth let wh window innerHeight let ww 600 let wh 400 let container document createElement div document body appendChild container container id container let opts document createElement div document body appendChild opts opts style position fixed opts style right 10px opts style top 10px function checkbox iargs id undefined checked undefined text undefined let el document getElementById iargs id if el el document createElement div el id iargs id el style border 1px solid gray opts appendChild el el appendChild document createElement label el appendChild document createElement input el children 0 style vertical align top el children 1 setAttribute type checkbox if iargs text el children 0 innerHTML iargs text if iargs checked el children 1 checked iargs checked el children 1 onchange setup return el children 1 checked checkbox id refract checked true text show refract rays checkbox id normals checked true text show normals checkbox id reflect checked false text show reflect rays checkbox id fresnel checked false text show fresnel magnitude function inputnumber iargs id undefined value undefined range undefined text undefined step undefined let el document getElementById iargs id if el el document createElement div el id iargs id el style border 1px solid gray opts appendChild el el appendChild document createElement label el appendChild document createElement input el children 0 style vertical align top el children 1 setAttribute type number el children 1 setAttribute min 1 el children 1 setAttribute type number if iargs text el children 0 innerHTML iargs text if iargs range el children 1 min iargs range 0 if iargs range el children 1 max iargs range 1 if iargs value el children 1 value iargs value if iargs step el children 1 step iargs step el children 1 onchange setup el children 1 onblur setup return el children 1 value inputnumber id numrays value 4 range 1 10 step 1 text number rays inputnumber id eta value 1 3 range 0 3 step 0 1 text eta inputnumber id maxlines value 70 range 1 100 step 1 text max lines inputnumber id maxbounces value 10 range 0 100 step 1 text max ray bounces inputnumber id numspheres value 3 range 1 5 step 1 text number spheres inputnumber id yfov value 5 range 1 5 step 1 text y fov spacing function setup container innerHTML let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width ww svg setAttributeNS null height wh svg setAttributeNS null fill currentColor svg style border 1px solid blue container appendChild svg function setCircle defs c undefined r undefined id undefined col green enabled true let newCircle document getElementById defs id if newCircle newCircle document createElementNS http www w3 org 2000 svg circle newCircle id defs id svg appendChild newCircle newCircle setAttribute cx defs c x newCircle setAttribute cy defs c y newCircle setAttribute r defs r newCircle setAttribute fill transparent newCircle setAttribute stroke width 2 newCircle setAttribute stroke defs col newCircle style display defs enabled block none setCircle x 200 y 100 50 c0 let shapes shapes push c x 250 y 205 r 55 id c0 type circle col green enabled true shapes push c x 200 y 90 r 50 id c1 type circle col orange enabled true shapes push c x 100 y 330 r 40 id c2 type circle col purple enabled true shapes push c x 350 y 300 r 15 id c3 type circle col magenta enabled true shapes push c x 390 y 60 r 25 id c4 type circle col yellow enabled true shapes forEach s setCircle c s c r s r id s id col s col function showNormal afs p undefined n undefined col black len 15 if afs col afs col black if afs len afs len 15 let n0 document createElementNS http www w3 org 2000 svg line n0 style color afs col n0 setAttribute stroke afs col let e add afs p scale afs n afs len svg appendChild n0 n0 setAttribute x1 afs p x n0 setAttribute y1 afs p y n0 setAttribute x2 e x n0 setAttribute y2 e y all this code just for an arrow head let arrowID arrow Math random let defs document createElementNS http www w3 org 2000 svg defs let marker document createElementNS http www w3 org 2000 svg marker marker setAttribute id arrowID marker setAttribute markerWidth 10 marker setAttribute markerHeight 7 marker setAttribute markerUnits strokeWidth marker setAttribute refX 0 warning case sensitive refx refX marker setAttribute refY 3 5 marker setAttribute orient auto let path document createElementNS http www w3 org 2000 svg path path setAttribute d M 0 0 L 10 3 5 L 0 7 z path setAttribute fill afs col arrow head marker appendChild path defs appendChild marker svg appendChild defs n0 setAttribute marker end url arrowID function setLine id s e opt let i0 document getElementById id if i0 null i0 document createElementNS http www w3 org 2000 svg line i0 id id var randomColor Math random 0xFFFFFF 0 toString 16 let rbyte return Math floor Math random 256 256 let randomColor rgb rbyte rbyte rbyte i0 setAttribute stroke randomColor svg appendChild i0 i0 setAttribute x1 s x i0 setAttribute y1 s y i0 setAttribute x2 e x i0 setAttribute y2 e y if typeof opt undefined Object entries opt forEach o const k v o i0 setAttribute k v function sub a b return x a x b x y a y b y function add a b return x a x b x y a y b y function dist a b return Math sqrt a x b x a x b x a y b y a y b y function norm a let d Math sqrt a x a x a y a y return x a x d y a y d function len a return Math sqrt a x a x a y a y function scale a s return x a x s y a y s function dot a b return a x b x a y b y function lineIntersectCircle line circle let s line s let e line e let r circle r let c circle c let tsc len sub s c let tec len sub e c if tsc r tec r inside sphere console log both s and e inside sphere return hit false let inside false if tec r inside true let nse norm sub e s let vsc sub c s let to dot nse vsc let th len vsc let ta Math sqrt th th to to if ta r missed sphere console log ray misses sphere return hit false let tpa Math sqrt r r ta ta let t to tpa if tsc r start inside the sphere t to tpa let tse len sub e s if t 0 t tse greater than length of line return hit false let p add s scale nse t let n norm sub p c return hit true normal n hitpoint p pen tse t dir nse inside inside function reflect i n I 2 0 dot N I N return norm sub scale i 1 scale n 2 dot n i source material index of refraction IOR destination material IOR function refract i n eta k 1 0 eta eta 1 0 dot N I dot N I if k 0 0 R vec 0 0 else R eta I eta dot N I sqrt k N let k 1 0 eta eta 1 0 dot n i dot n i if k 0 0 normal and the incident are tangental k 0 01 let s eta dot n i Math sqrt k return norm sub scale i eta scale n s let lines add point light let p0 x 50 y 50 for let k 0 k 5 k let sin Math sin let cos Math cos let t Math PI 2 k 5 0 1 let n x sin t y cos t let e add p0 n let ii id iv k s p0 e e speed 3 alive true lines push ii setLine ii id ii s ii e let origin x 20 y 200 let target x 50 y 200 let forward norm sub target origin let up x forward y y forward x let numrays inputnumber id numrays let yfov inputnumber id yfov lines push id ic0 s origin e target speed 5 alive true depth 0 setCircle c origin r 2 id cc0o col black enabled true setCircle c target r 2 id cc0t col black enabled true for let n 1 n numrays n let eu add target scale up n yfov let ed add target scale up n yfov lines push id icu n s origin e eu speed 5 alive true depth 0 lines push id icd n s origin e ed speed 5 alive true depth 0 setCircle c eu r 2 id cc1 n col black enabled true setCircle c ed r 2 id cc2 n col black enabled true function fresnel c1 c2 i n e g color reflectionColor f refractionColor 1 f Schlicks approximation R theta R0 1 R0 1 cos theta 5 0 theta 90 R0 n1 n2 n1 n2 2 let r0 Math pow c1 c2 c1 c2 2 let cosX dot n i if c1 c2 let s c1 c2 let sinT2 s s 1 cosX cosX if sinT2 1 0 return 1 0 cosX Math sqrt 1 0 sinT2 return r0 1 r0 Math pow 1 cosX 1 1 5 5 defaut amplify the visual setting the pow to 1 makes the curve into an inverse of the dot function updaterays if lines length inputnumber id maxlines throw max lines reached lines length status innerHTML Lines lines length shapes forEach s i s enabled true if i inputnumber id numspheres s enabled false setCircle s lines forEach line let hit false if line alive false return if typeof line depth undefined throw line without depth data if line depth inputnumber id maxbounces return shapes forEach sh if sh enabled return let res lineIntersectCircle line sh if res hit if checkbox id normals showNormal p res hitpoint n res normal line e res hitpoint setLine line id line s line e let svgCircle document getElementById c0 svgCircle setAttribute stroke red let i norm sub line e line s showNormal p line e n scale i 1 c green if checkbox id fresnel let eta inputnumber id eta let f fresnel 1 0 eta scale i 1 res normal f dot i res normal showNormal p res hitpoint n scale res normal f col red len f 50 refraction transparent through the object if checkbox id refract let normal res normal if res inside inside to outside normal scale normal 1 another way of checking inverting the normal you could also use dot i n 0 means leaving the sphere if dot i n 0 res inside showNormal p line e n normal c blue eta is the ratio between the refractive index of the medium being left air is 1 and the medium being entered Once you enter an object and hit the back side you need to refract by 1 eta basically let eta inputnumber id eta if res inside eta 1 eta let rf refract i normal eta showNormal p line e n rf col purple showNormal p res hitpoint n res dir col red const s0 add res hitpoint scale res dir 1 const e0 add s0 scale rf 1 0 const newline id refa lines length s s0 e e0 speed 5 alive true depth line depth 1 lines push newline setCircle c line e r 2 id cc0 Math random col black enabled true showNormal p newline s n rf col purple if res inside setLine newline id newline s newline e opt stroke dasharray 4 reflected bounce off the object if checkbox id reflect if res inside outside inside let rl reflect i res normal let s0 add res hitpoint scale res dir 1 let e0 add s0 scale rl 1 0 let newline id refb lines length s s0 e e0 speed 5 alive true depth line depth 1 showNormal p s0 n scale rl 1 lines push newline line alive false hit true return end foreach shapes if hit return let d dist line e line s line e add line s scale norm sub line e line s d line speed setLine line id line s line e if line e x ww line e y wh line e x 0 line e y 0 console log new line line alive false let n scale norm sub line e line s line speed 0 5 if line e y 0 line e y wh n y 1 if line e x 0 line e x ww n x 1 let ee add line e scale n 1 0 let newline id id lines length s line e e ee speed 5 alive true depth line depth 1 lines push newline end forEach for let g 0 g 1000 g clearInterval g let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 onclick updaterays end setup window onload setup console log ready
hit false let tpa Math sqrt r r ta ta let t to tpa if tsc r start inside the sphere t to tpa let tse len sub e s if t 0 t tse greater than length of line return hit false let p add s scale nse t let n norm sub p c return hit true normal n hitpoint p pen tse t dir nse inside inside function reflect i n I 2 0 dot N I N return norm sub scale i 1 scale n 2 dot n i source material index of refraction IOR destination material IOR function refract i n eta k 1 0 eta eta 1 0 dot N I dot N I if k 0 0 R vec 0 0 else R eta I eta dot N I sqrt k N let k 1 0 eta eta 1 0 dot n i dot n i if k 0 0 normal and the incident are tangental k 0 01 let s eta dot n i Math sqrt k return norm sub scale i eta scale n s let lines add point light let p0 x 50 y 50 for let k 0 k 5 k let sin Math sin let cos Math cos let t Math PI 2 k 5 0 1 let n x sin t y cos t let e add p0 n let ii id iv k s p0 e e speed 3 alive true lines push ii setLine ii id ii s ii e let origin x 20 y 200 let target x 50 y 200 let forward norm sub target origin let up x forward y y forward x let numrays inputnumber id numrays let yfov inputnumber id yfov lines push id ic0 s origin e target speed 5 alive true depth 0 setCircle c origin r 2 id cc0o col black enabled true setCircle c target r 2 id cc0t col black enabled true for let n 1 n numrays n let eu add target scale up n yfov let ed add target scale up n yfov lines push id icu n s origin e eu speed 5 alive true depth 0 lines push id icd n s origin e ed speed 5 alive true depth 0 setCircle c eu r 2 id cc1 n col black enabled true setCircle c ed r 2 id cc2 n col black enabled true function fresnel c1 c2 i n e g color reflectionColor f refractionColor 1 f Schlicks approximation R theta R0 1 R0 1 cos theta 5 0 theta 90 R0 n1 n2 n1 n2 2 let r0 Math pow c1 c2 c1 c2 2 let cosX dot n i if c1 c2 let s c1 c2 let sinT2 s s 1 cosX cosX if sinT2 1 0 return 1 0 cosX Math sqrt 1 0 sinT2 return r0 1 r0 Math pow 1 cosX 1 1 5 5 defaut amplify the visual setting the pow to 1 makes the curve into an inverse of the dot function updaterays if lines length inputnumber id maxlines throw max lines reached lines length status innerHTML Lines lines length shapes forEach s i s enabled true if i inputnumber id numspheres s enabled false setCircle s lines forEach line let hit false if line alive false return if typeof line depth undefined throw line without depth data if line depth inputnumber id maxbounces return shapes forEach sh if sh enabled return let res lineIntersectCircle line sh if res hit if checkbox id normals showNormal p res hitpoint n res normal line e res hitpoint setLine line id line s line e let svgCircle document getElementById c0 svgCircle setAttribute stroke red let i norm sub line e line s showNormal p line e n scale i 1 c green if checkbox id fresnel let eta inputnumber id eta let f fresnel 1 0 eta scale i 1 res normal f dot i res normal showNormal p res hitpoint n scale res normal f col red len f 50 refraction transparent through the object if checkbox id refract let normal res normal if res inside inside to outside normal scale normal 1 another way of checking inverting the normal you could also use dot i n 0 means leaving the sphere if dot i n 0 res inside showNormal p line e n normal c blue eta is the ratio between the refractive index of the medium being left air is 1 and the medium being entered Once you enter an object and hit the back side you need to refract by 1 eta basically let eta inputnumber id eta if res inside eta 1 eta let rf refract i normal eta showNormal p line e n rf col purple showNormal p res hitpoint n res dir col red const s0 add res hitpoint scale res dir 1 const e0 add s0 scale rf 1 0 const newline id refa lines length s s0 e e0 speed 5 alive true depth line depth 1 lines push newline setCircle c line e r 2 id cc0 Math random col black enabled true showNormal p newline s n rf col purple if res inside setLine newline id newline s newline e opt stroke dasharray 4 reflected bounce off the object if checkbox id reflect if res inside outside inside let rl reflect i res normal let s0 add res hitpoint scale res dir 1 let e0 add s0 scale rl 1 0 let newline id refb lines length s s0 e e0 speed 5 alive true depth line depth 1 showNormal p s0 n scale rl 1 lines push newline line alive false hit true return end foreach shapes if hit return let d dist line e line s line e add line s scale norm sub line e line s d line speed setLine line id line s line e if line e x ww line e y wh line e x 0 line e y 0 console log new line line alive false let n scale norm sub line e line s line speed 0 5 if line e y 0 line e y wh n y 1 if line e x 0 line e x ww n x 1 let ee add line e scale n 1 0 let newline id id lines length s line e e ee speed 5 alive true depth line depth 1 lines push newline end forEach for let g 0 g 1000 g clearInterval g let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 onclick updaterays end setup window onload setup console log ready