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document body style minHeight 200px let svg document createElementNS http www w3 org 2000 svg svg svg width 200 svg height 200 svg style border 1px solid blue document body appendChild svg var newLine document createElementNS http www w3 org 2000 svg line newLine id i0 newLine setAttribute x1 10 newLine setAttribute y1 10 newLine setAttribute x2 100 newLine setAttribute y2 50 newLine setAttribute stroke orange svg appendChild newLine let i0 document getElementById i0 console log i0 i0 i0 setAttribute stroke red document body style minHeight 200px let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width 400 svg setAttributeNS null height 400 svg style border 1px solid blue document body appendChild svg var newLine document createElementNS http www w3 org 2000 svg line newLine id i0 newLine setAttribute x1 10 newLine setAttribute y1 10 newLine setAttribute x2 100 newLine setAttribute y2 190 newLine setAttribute stroke orange svg appendChild newLine let i0 document getElementById i0 console log i0 i0 i0 setAttribute stroke red function setLine id s e let i0 document getElementById id if i0 null i0 document createElementNS http www w3 org 2000 svg line i0 id id var randomColor Math floor Math random 16777215 toString 16 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 let ww window innerWidth let wh window innerHeight function sub a b return x b x a x y b y a 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 scale a s return x a x s y a y s let ray o x 10 y 10 d x 0 2 y 0 5 l 0 let ii id i0 s x 10 y 10 e x 50 y 100 speed 5 alive true setLine ii id ii s ii e let lines ii function updaterays if lines length 20 throw max 20 lines reached lines forEach line if line alive false 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready document body style minHeight 200px let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width 400 svg setAttributeNS null height 400 svg style border 1px solid blue document body appendChild svg var newLine document createElementNS http www w3 org 2000 svg line newLine id i0 newLine setAttribute x1 10 newLine setAttribute y1 10 newLine setAttribute x2 100 newLine setAttribute y2 190 newLine setAttribute stroke orange svg appendChild newLine 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 col svg appendChild newCircle addCircle x 200 y 100 50 c0 let shapes shapes push c x 300 y 200 r 50 id c0 type circle shapes push c x 100 y 300 r 20 id c0 type circle shapes forEach s addCircle s c s r s id let i0 document getElementById i0 console log i0 i0 i0 setAttribute stroke red function setLine id s e let i0 document getElementById id if i0 null i0 document createElementNS http www w3 org 2000 svg line i0 id id var randomColor Math floor Math random 16777215 toString 16 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 let ww window innerWidth let wh window innerHeight function sub a b return x b x a x y b y a 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 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 n norm sub line e circle c return hit true normal n hitpoint line e 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 sub scale i 1 scale n 2 dot n i let ii id i0 s x 10 y 10 e x 50 y 100 speed 5 alive true setLine ii id ii s ii e let lines ii function updaterays if lines length 20 throw max 20 lines reached lines forEach line let hit false if line alive false return shapes forEach s let res lineIntersectCircle line s if res hit let svgCircle document getElementById c0 svgCircle setAttribute fill red let i norm sub line e line s let r reflect i res normal let s0 add line e scale r 5 0 let e0 add line e scale r 6 0 let newline id ref lines length s s0 e e0 speed 5 alive true 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready document body style minHeight 200px let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width 400 svg setAttributeNS null height 400 svg style border 1px solid blue document body appendChild svg var newLine document createElementNS http www w3 org 2000 svg line newLine id i0 newLine setAttribute x1 10 newLine setAttribute y1 10 newLine setAttribute x2 100 newLine setAttribute y2 190 newLine setAttribute stroke orange svg appendChild newLine 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 col svg appendChild newCircle addCircle x 200 y 100 50 c0 let shapes shapes push c x 300 y 200 r 50 id c0 type circle shapes push c x 100 y 300 r 20 id c0 type circle shapes forEach s addCircle s c s r s id function setLine id s e let i0 document getElementById id if i0 null i0 document createElementNS http www w3 org 2000 svg line i0 id id var randomColor Math floor Math random 16777215 toString 16 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 let ww window innerWidth let wh window innerHeight function sub a b return x b x a x y b y a 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 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 n norm sub line e circle c return hit true normal n hitpoint line e 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 sub scale i 1 scale n 2 dot n i 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 function updaterays if lines length 40 throw max 20 lines reached lines forEach line let hit false if line alive false return shapes forEach s let res lineIntersectCircle line s if res hit let svgCircle document getElementById c0 svgCircle setAttribute fill red let i norm sub line e line s let r reflect i res normal let s0 add line e scale r 5 0 let e0 add line e scale r 6 0 let newline id ref lines length s s0 e e0 speed 5 alive true 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready Left in the bug for previous iterations above but have fixed it below as an example of just how easy a small typo due to copy and pasting can lead to serious bugs and problems later on As the simulation seems to work but as you start to elaborate and do more testing you notice something isn t correct For example the refraction index should be a straight line when both material indexes are the same should not bend Of course during testing the maths didn t seem to add up this was due to a bug in the add and sub functions An incorrect sign also the order of subtraction left to right wasn t correct Fixed in the below example needs changing in two places so that it continues to work but extra features function correction without strange anomalies document body style minHeight 200px let status document createElement div status innerHTML Lines document body appendChild status let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width 400 svg setAttributeNS null height 400 svg setAttributeNS null fill currentColor svg style border 1px solid blue document body appendChild svg var defs document createElementNS http www w3 org 2000 svg defs svg appendChild defs defs innerHTML marker id arrowhead markerWidth 10 markerHeight 7 refX 0 refY 3 5 orient auto polygon points 0 0 10 3 5 0 7 marker 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 30 id c2 type circle shapes forEach s addCircle s c s r s id function showNormal p n col black let n0 document createElementNS http www w3 org 2000 svg line n0 style color col n0 setAttribute stroke col let e add p scale n 15 0 svg appendChild n0 n0 setAttribute x1 p x n0 setAttribute y1 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 let id arrowID marker setAttribute id id 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 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 00 Math floor Math random 16777215 toString 16 substring 0 4 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 let ww window innerWidth let wh window innerHeight 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 lines push id iv0 s x 20 y 45 e x 60 y 60 speed 5 alive true function updaterays if lines length 30 throw max lines reached lines length status innerHTML Lines lines length lines forEach line let hit false if line alive false return shapes forEach s let res lineIntersectCircle line s if res hit showNormal res hitpoint 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 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 line e normal blue showNormal line e i 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 1 5 if res inside eta 1 eta let rf refract i normal eta showNormal line e rf let hp add res hitpoint scale norm sub line e line s 2 0 showNormal hp 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 lines push newline if res inside setLine newline id newline s newline e opt stroke dasharray 4 reflected bounce off the object if res inside outside inside let rl reflect i res normal let s0 add line e scale norm sub line e line s 1 0 let e0 add s0 scale rl 2 0 let newline id refb lines length s s0 e e0 speed 5 alive true showNormal s0 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach window onclick function updaterays let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready style document body style minHeight 400px style Refraction https notebook xbdev net var images imgIwUTQxZa6eE2 jpg

5 0 let e0 add line e scale r 6 0 let newline id ref lines length s s0 e e0 speed 5 alive true 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready Left in the bug for previous iterations above but have fixed it below as an example of just how easy a small typo due to copy and pasting can lead to serious bugs and problems later on As the simulation seems to work but as you start to elaborate and do more testing you notice something isn t correct For example the refraction index should be a straight line when both material indexes are the same should not bend Of course during testing the maths didn t seem to add up this was due to a bug in the add and sub functions An incorrect sign also the order of subtraction left to right wasn t correct Fixed in the below example needs changing in two places so that it continues to work but extra features function correction without strange anomalies document body style minHeight 200px let status document createElement div status innerHTML Lines document body appendChild status let svg document createElementNS http www w3 org 2000 svg svg svg setAttributeNS null width 400 svg setAttributeNS null height 400 svg setAttributeNS null fill currentColor svg style border 1px solid blue document body appendChild svg var defs document createElementNS http www w3 org 2000 svg defs svg appendChild defs defs innerHTML marker id arrowhead markerWidth 10 markerHeight 7 refX 0 refY 3 5 orient auto polygon points 0 0 10 3 5 0 7 marker 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 30 id c2 type circle shapes forEach s addCircle s c s r s id function showNormal p n col black let n0 document createElementNS http www w3 org 2000 svg line n0 style color col n0 setAttribute stroke col let e add p scale n 15 0 svg appendChild n0 n0 setAttribute x1 p x n0 setAttribute y1 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 let id arrowID marker setAttribute id id 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 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 00 Math floor Math random 16777215 toString 16 substring 0 4 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 let ww window innerWidth let wh window innerHeight 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 lines push id iv0 s x 20 y 45 e x 60 y 60 speed 5 alive true function updaterays if lines length 30 throw max lines reached lines length status innerHTML Lines lines length lines forEach line let hit false if line alive false return shapes forEach s let res lineIntersectCircle line s if res hit showNormal res hitpoint 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 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 line e normal blue showNormal line e i 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 1 5 if res inside eta 1 eta let rf refract i normal eta showNormal line e rf let hp add res hitpoint scale norm sub line e line s 2 0 showNormal hp 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 lines push newline if res inside setLine newline id newline s newline e opt stroke dasharray 4 reflected bounce off the object if res inside outside inside let rl reflect i res normal let s0 add line e scale norm sub line e line s 1 0 let e0 add s0 scale rl 2 0 let newline id refb lines length s s0 e e0 speed 5 alive true showNormal s0 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 400 line e y 400 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 400 n y 1 if line e x 0 line e x 400 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 lines push newline end forEach window onclick function updaterays let count 0 let iid setInterval try count if count 15000 clearInterval iid updaterays catch e console log error e clearInterval iid 50 console log ready style document body style minHeight 400px style Refraction https notebook xbdev net var images imgIwUTQxZa6eE2 jpg

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