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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 false text show refract rays checkbox id normals checked true text show normals checkbox id reflect checked true text show reflect rays 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 3 range 1 6 step 1 text number rays inputnumber id eta value 1 3 range 0 3 step 0 1 text eta inputnumber id maxlines value 40 range 1 100 step 1 text max lines inputnumber id maxbounces value 10 range 0 100 step 1 text max ray bounces 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 addCircle c r id col green var newCircle document createElementNS http www w3 org 2000 svg circle newCircle id id newCircle setAttribute cx c x newCircle setAttribute cy c y newCircle setAttribute r r newCircle setAttribute fill transparent newCircle setAttribute stroke width 2 newCircle setAttribute stroke col svg appendChild newCircle addCircle x 200 y 100 50 c0 let shapes shapes push c x 160 y 110 r 50 id c0 type circle shapes push c x 100 y 330 r 40 id c1 type circle shapes push c x 250 y 230 r 35 id c2 type circle shapes forEach s addCircle s c s r s id function showNormal afs p undefined n undefined col black if afs col afs col black 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 15 0 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 n0 setAttribute marker end url arrowhead 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 d0 dist line s circle c let d1 dist line e circle c let d0inside d0 circle r let d1inside d1 circle r if d0inside d1inside let pen circle r d1 d0 d1 d0 let n norm sub line e circle c let hitpoint add line e scale norm sub line e line s pen 1 5 return hit true normal n hitpoint hitpoint inside d1inside pen pen return hit false normal x 0 y 0 hitpoint x 0 y 0 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 efov 3 lines push id ic0 s origin e target speed 5 alive true depth 0 addCircle origin 2 cc0 col black for let n 1 n numrays n let eu add target scale up n efov let ed add target scale up n efov 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 addCircle eu 2 cc0 col black addCircle ed 2 cc0 col black function updaterays if lines length inputnumber id maxlines throw max lines reached lines length status innerHTML Lines lines length 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 s let res lineIntersectCircle line s 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 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 col blue showNormal p line e n i col red 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 let hp add res hitpoint scale norm sub line e line s 3 0 showNormal p hp n rf let s0 hp let e0 add hp scale rf 2 0 let newline id refa lines length s s0 e e0 speed 5 alive true depth line depth 1 lines push newline 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 line e scale norm sub line e line s 3 0 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 s line e 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 end setup window onload setup console log ready 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 false text show refract rays checkbox id normals checked false text show normals checkbox id reflect checked false text show reflect rays checkbox id fresnel checked true 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 20 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 40 range 1 100 step 1 text max lines inputnumber id maxbounces value 0 range 0 100 step 1 text max ray bounces inputnumber id numspheres value 1 range 1 5 step 1 text number spheres inputnumber id yfov value 0 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 n0 setAttribute marker end url arrowhead 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 d0 dist line s circle c let d1 dist line e circle c let d0inside d0 circle r let d1inside d1 circle r if d0inside d1inside let pen circle r d1 d0 d1 d0 let n norm sub line e circle c let hitpoint add line e scale norm sub line e line s pen 1 5 return hit true normal n hitpoint hitpoint inside d1inside pen pen return hit false normal x 0 y 0 hitpoint x 0 y 0 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 cc0 col black 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 cc0 col black setCircle c ed r 2 id cc0 col black 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 s if s enabled return let res lineIntersectCircle line s 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 let hp add res hitpoint scale norm sub line e line s 3 0 showNormal p hp n rf let s0 hp let e0 add hp scale rf 2 0 let newline id refa lines length s s0 e e0 speed 5 alive true depth line depth 1 lines push newline 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 line e scale norm sub line e line s 3 0 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 s line e 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 end setup window onload setup console log ready

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 false text show refract rays checkbox id normals checked false text show normals checkbox id reflect checked false text show reflect rays checkbox id fresnel checked true 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 20 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 40 range 1 100 step 1 text max lines inputnumber id maxbounces value 0 range 0 100 step 1 text max ray bounces inputnumber id numspheres value 1 range 1 5 step 1 text number spheres inputnumber id yfov value 0 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 n0 setAttribute marker end url arrowhead 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 d0 dist line s circle c let d1 dist line e circle c let d0inside d0 circle r let d1inside d1 circle r if d0inside d1inside let pen circle r d1 d0 d1 d0 let n norm sub line e circle c let hitpoint add line e scale norm sub line e line s pen 1 5 return hit true normal n hitpoint hitpoint inside d1inside pen pen return hit false normal x 0 y 0 hitpoint x 0 y 0 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 cc0 col black 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 cc0 col black setCircle c ed r 2 id cc0 col black 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 s if s enabled return let res lineIntersectCircle line s 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 let hp add res hitpoint scale norm sub line e line s 3 0 showNormal p hp n rf let s0 hp let e0 add hp scale rf 2 0 let newline id refa lines length s s0 e e0 speed 5 alive true depth line depth 1 lines push newline 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 line e scale norm sub line e line s 3 0 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 s line e 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 end setup window onload setup console log ready

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