MIME-Version: 1.0 Date: Mon, 12 Oct 2020 16:33:27 -0300 References: In-Reply-To: Message-ID: Subject: Re: Photon Mapping - dudas sobre el color y avances From: =?UTF-8?Q?Eduardo_Fern=C3=A1ndez?= To: Paula Cc: Leonardo Fallini , Jose Pedro Aguerre Content-Type: multipart/mixed; boundary="00000000000041d58205b17e5f5e" --00000000000041d58205b17e5f5e Content-Type: multipart/related; boundary="00000000000041d58105b17e5f5d" --00000000000041d58105b17e5f5d Content-Type: multipart/alternative; boundary="00000000000041d58005b17e5f5c" --00000000000041d58005b17e5f5c Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Hola, La ley del coseno se aplica para la luz emisora difusa superficial. Al emisor puntual que flota en el espacio se aplica el c=C3=B3digo del slide 1= 2. Pero recomiento usar algo con quasinumbers, para que tenga una distribuci= =C3=B3n m=C3=A1s "pareja", sin huecos ni concentraciones. Pens=C3=A9 que en el caso de ustedes era un emisor difuso de superficie, po= r lo que se ve reflejado en la esfera espejada. No entiendo la forma que tiene esa distribuci=C3=B3n que es como una semies= fera pero con puntas. El c=C3=B3digo para generar un emisor que siga la ley de coseno, es el del = link que les mand=C3=A9 en un mensaje del foro. El peor caso es el que les mando ahora. %% Distribuci=C3=B3n uniforme. La peor de todas(pero s=C3=B3lo 6 l=C3=ADnea= s de c=C3=B3digo sin contar lo gr=C3=A1fico). figure; hold on for i=3D1:10000 rho=3Dsqrt(rand); theta=3Drand*2*pi; [x,y]=3Dpol2cart(theta,rho); z=3Dsqrt(1-x^2-y^2); plot3(x,y,z,':'); end axis('square') Tambi=C3=A9n les mando una imagen de c=C3=B3mo se genera. Como ven hacia ar= riba se emiten m=C3=A1s fotones, y hacia el lado inferior de la semiesfera se emite= n menos fotones. saludos, Eduardo On Mon, Oct 12, 2020 at 2:55 PM Paula wrote: > Hola Eduardo, > muchas gracias por la respuesta, nos aclar=C3=B3 bastante y luego estarem= os > probando las distintas formas de tratar la luz y el color de los fotones > para ver cu=C3=A1l es la m=C3=A1s adecuada para el caso. Por otro lado, n= o tenemos > problema que se publiquen en el foro las dudas. > > Respecto a las direcciones de la emisi=C3=B3n de fotones, justo est=C3=A1= bamos > probando eso y ahora nos surgi=C3=B3 la duda, =C2=BFdesde el punto de la = luz tienen > que ser emitidos con la ley del coseno? Porque nosotros est=C3=A1bamos ap= licando > (o al menos intentando) la ley del coseno para el caso que un fot=C3=B3n = en la > ruleta rusa entre en el caso de difusi=C3=B3n. Para el caso de la luz (qu= e por > el momento es =C3=BAnicamente un punto y no un =C3=A1rea), est=C3=A1bamos= emitiendo las > direcciones con n=C3=BAmeros quasi-random y en la semiesfera que da al cu= arto. > Otra aclaraci=C3=B3n es que en la imagen, la ubicaci=C3=B3n de la luz en= este caso > no est=C3=A1 en el centro del cuarto sino que un poco por encima de la c= =C3=A1mara. > > Por otro lado, est=C3=A1bamos viendo si la forma que aplicamos la ley del > coseno estaba correcta. Intentamos replicar en python el c=C3=B3digo del = eva > para la ley del coseno y obtuvimos el siguiente resultado: > [image: image.png] > esta ser=C3=ADa la forma del cono? Nos imaginamos que iba a tener una for= ma > distinta, m=C3=A1s parecida a un cono o un globo. Si esta es la forma, d= =C3=B3nde > estar=C3=ADa el origen de la emisi=C3=B3n? > > Nuevamente muchas gracias! > > > El lun., 12 de oct. de 2020 a la(s) 12:47, Eduardo Fern=C3=A1ndez ( > edufer111@gmail.com) escribi=C3=B3: > >> Un =C3=BAltimo comentario sobre las im=C3=A1genes. Quiz=C3=A1 es una ilu= si=C3=B3n, pero me >> parece que el emisor no emite seg=C3=BAn la ley del coseno. Veo que las = paredes >> est=C3=A1n muy iluminadas contra el techo, que le llega igual cantidad d= e >> fotones en toda su superficie. Quiz=C3=A1 es s=C3=B3lo una impresi=C3=B3= n. >> Eduardo >> >> On Mon, Oct 12, 2020 at 11:32 AM Eduardo Fern=C3=A1ndez >> wrote: >> >>> Hola Paula y Leonardo, >>> >>> On Sun, Oct 11, 2020 at 9:31 PM Paula wrote: >>> >>>> Buenas noches, >>>> esperamos no molestar debido al d=C3=ADa y hora pero tenemos una duda = y nos >>>> gustar=C3=ADa plantearla, si no nos pueden responder antes de la clase= no hay >>>> problema lo vemos ah=C3=AD. >>>> Estuvimos probando cosas pero no logramos entender del todo el manejo >>>> de potencia, colores y coeficientes difusos. Esto ser=C3=ADa para luce= s, fotones >>>> y superficies. (en los siguientes p=C3=A1rrafos, cuando decimos que al= go tiene >>>> color, nos referimos a un vector3 rgb con valores de 0 a 1.) >>>> >>> >>> Estuve pensando y el tema de la potencia (dividir la potencia total por >>> los fotones, etc.) en realidad es algo confuso y que no es =C3=BAtil. J= ensen nos >>> hace confundir con esas explicaciones, de dividir la potencia en los >>> fotones. Lo que importa es la relaci=C3=B3n entre las luces de las supe= rficies. >>> Todos sabemos que si una foto sale oscura, con una c=C3=A1mara m=C3=A1s= sensible >>> saldr=C3=A1 m=C3=A1s brillante (o con m=C3=A1s tiempo de exposici=C3=B3= n). Y lo que queremos >>> siempre es ver bien la imagen. En nuestro caso, si vemos una foto oscur= a o >>> brillante, la podemos "arreglar" multiplicando los p=C3=ADxeles por la = constante >>> adecuada, o por la funci=C3=B3n adecuada, para lograr ver la imagen cla= ramente. >>> >>> Lo que importa es que si tengo dos l=C3=A1mparas, por ejemplo una con 1= 00W y >>> otra con 50W, entonces la primera emite el doble de fotones que la segu= nda. >>> En ambas l=C3=A1mparas, los fotones emitidos tienen la misma potencia. = Lo que >>> define la potencia de cada l=C3=A1mpara es la cantidad de fotones emiti= dos por >>> cada una. Luego, cuando se tiene el mapa de fotones y se va a generar l= a >>> imagen, entonces lo que importa, lo que define la intensidad de la luz = en >>> las superficies es la cantidad de fotones por unidad de =C3=A1rea. Si e= n la >>> superficie B hay 1 fot=C3=B3n por unidad de =C3=A1rea y en la superfici= e C hay 10 >>> fotones por unidad de =C3=A1rea, entonces C debe lucir 10 veces m=C3=A1= s brillante >>> que B. Nuestro algoritmo har=C3=A1 los ajustes pertinentes para que la = imagen >>> salga n=C3=ADtida. >>> >>> >>>> *Luces: *En primer lugar, lo que estamos haciendo es dividir la >>>> potencia de la luz entre la cantidad de fotones y llamamos a la funci= =C3=B3n >>>> recursiva que emite y almacena los fotones con el resultado de la divi= si=C3=B3n >>>> guardado en un vec3. Por ahora ponemos la misma potencia para cada col= or ya >>>> que estamos probando pero no tenemos claro que si queremos que la luz = tenga >>>> cierto color qu=C3=A9 es lo que debemos hacer (capaz que tener un colo= r para la >>>> luz y ponderarlo por la potencia, o tener potencia distinta para cada >>>> color?). >>>> >>> >>> Cuando la luz es solo potencia, sin color, los fotones claramente >>> mantienen la misma potencia en cada "rebote". >>> Yo probar=C3=ADa poni=C3=A9ndole a cada fot=C3=B3n el color (1,1,1) cua= ndo la luz >>> emitida es blanca y el (r,g,b) adecuado entre 0 y 1 cuando tiene color.= Si >>> la luz es roja, entonces el color ser=C3=ADa (1,0,0) y ver=C3=ADa el ef= ecto que >>> genera. Si hay una l=C3=A1mpara B de luz Blanca con 100W y una l=C3=A1m= para R de 50W >>> con luz roja, y el total de fotones es 15000, entonces B emitir=C3=ADa = 10000 >>> fotones con color (1,1,1) y R emitir=C3=ADa 5000 fotones con color (1,0= ,0). Se >>> puede afinar m=C3=A1s (por ejemplo que el m=C3=B3dulo o norma del vecto= r color sea >>> siempre 1, cosa que los fotones tengan la misma "potencia", y por tanto= los >>> fotones blancos deber=C3=ADan tener valores [sqrt(1/3), sqrt(1/3), sqrt= (1/3)] ) >>> pero me parece que para una primera aproximaci=C3=B3n est=C3=A1 m=C3=A1= s que bien. >>> >>> >>>> *Fotones:* En las diapositivas dice que la potencia es un char de 4 >>>> valores pero en la clase dijeron que eso se pod=C3=ADa usar con tres v= alores o >>>> como nos quede m=C3=A1s c=C3=B3modo. En este caso entonces la potencia= equivale al >>>> color del fot=C3=B3n y no se deber=C3=ADa tener nada m=C3=A1s? Es deci= r, un vec3 con un >>>> valor para cada color entre 0 y 1. Como este color va cambiando cu=C3= =A1ndo un >>>> foton "rebota" (entendemos que no es que rebote sino que ser=C3=ADa un= fot=C3=B3n >>>> nuevo) debido al sangrado no entendemos como se puede respetar "que t= odos >>>> los fotones tengan la misma potencia" o quizas se refiere =C3=BAnicame= nte a los >>>> emitidos inicialmente por la luz. >>>> >>> >>> Cuando las paredes tienen color, y se genera el cambio de color de los >>> fotones que "rebotan", la cuenta que se hace es la especificada en los >>> slides 28 y 29. Sobre si mantiene o no la misma potencia, la respuesta = es >>> NO, si se hacen las cuentas de los slides 28 y 29. >>> Para mi la cuenta adecuada, que mantendr=C3=ADa la potencia de cada fot= =C3=B3n >>> luego del rebote deber=C3=ADa ser: >>> >>> Pinc=3D(Pr,Pg,Pb), power of the incident photon >>> S=3D(Sr,Sg,Sb), specular reflectance >>> D=3D(Dr,Dg,Db), diffuse reflectance >>> then >>> Ps=3D||(SrPr,SgPg,SbPb)||/||Pinc|| where || || is the 2-norm and Ps is >>> the probability of specular reflection >>> Pd=3D||(DrPr,DgPg,DbPb)||/||Pinc|| where Pd is the probability of >>> diffuse reflection >>> and also >>> Prefl,s=3D(SrPr,SgPg,SbPb)/Ps power of reflected specular photon >>> Prefl,d=3D(DrPr,DgPg,DbPb)/Pd power of reflected diffuse photon >>> >>> Est=C3=A1 en ingl=C3=A9s porque lo saqu=C3=A9 de un mail que le mand=C3= =A9 a Jensen y que >>> todav=C3=ADa espero respuesta :-). >>> >>> Si tienen ganas podr=C3=ADan probar mi cuenta y la de Jensen y comparar >>> diferencias (yo no la prob=C3=A9 en un algoritmo de PM). Hay un peque= =C3=B1o cambio >>> en el c=C3=A1lculo de Ps y Pd, y mi pregunta es por qu=C3=A9 Jensen usa= max (norma >>> infinito) en lugar de norma 2. Sospecho que es para hacer cuentas m=C3= =A1s >>> r=C3=A1pidas y no usar raiz cuadrada. Y quiz=C3=A1 ambas aproximaciones= convergen a >>> la misma imagen (es lo que no s=C3=A9 y me gustar=C3=ADa probar). Pero = sospecho que >>> usar norma 2 es m=C3=A1s eficiente en cuanto a almacenamiento porque ev= ita la >>> posibilidad de guardar fotones con muy poca energ=C3=ADa, fotones que i= nfluyen >>> poco en el resultado final. >>> >>> >>>> *Superficies:* finalmente, en este caso es el que posiblemente tenemos >>>> m=C3=A1s dudas de c=C3=B3mo implementarlo. Entendemos que se tiene un = kdr, kdg y kdb >>>> (lo mismo con especular). Estos coeficientes, que ser=C3=ADan exactame= nte? >>>> Porque a cada superficie(o mejor dicho cada primitiva) le estamos asig= nando >>>> un color ( vec3 de 0 a 1). No entendemos cu=C3=A1l ser=C3=ADa la difer= encia o >>>> relaci=C3=B3n entre el color y los kd para cada color. O mejor dicho, = este >>>> "color" que le estamos asignando a la superficie ya representa los kd = para >>>> cada color? >>>> >>> >>> No entend=C3=AD por qu=C3=A9 ponen la letra k delante. En los slides de= l curso es >>> (dr,dg,db). Pero S=C3=8D, el color de la superficie es el (dr,dg,db). >>> >>> >>>> Tenemos m=C3=A1s dudas pero esta es una que nos aclarar=C3=ADa bastant= e y ya >>>> podr=C3=ADamos emprolijarlo en el c=C3=B3digo ya que estuvimos medio q= ue usando el >>>> color como el kd para cada componente.. >>>> >>>> Adjuntamos tambi=C3=A9n un par de im=C3=A1genes para que vean como est= amos >>>> emitiendo los fotones. La primera es del mapa de fotones(200000) y la >>>> segunda es el resultado de ese mapa en la imagen. (Probablemente agreg= uemos >>>> algo de fatt en el algoritmo de Ray Tracing ya que se nos est=C3=A1n q= uemando un >>>> poco los objetos muy cercanos a la luz) >>>> >>>> [image: image.png] >>>> >>>> [image: image.png] >>>> >>>> Muchas gracias! Nos vemos ma=C3=B1ana en la consulta. >>>> >>> >>> Muy buenas las im=C3=A1genes. Se nota que hay un poco de sangrado, si s= e >>> notase m=C3=A1s ser=C3=ADa mejor. >>> Nos vemos hoy. >>> >>> saludos >>> Eduardo >>> >>> ps. =C2=BFLes parece bien mandar el mail de ustedes y mi respuesta al f= oro >>> del curso? As=C3=AD todos manejamos los mismos conceptos. La idea es qu= e todos >>> aprendamos de todos. >>> >>> >>> --00000000000041d58005b17e5f5c Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hola,
La ley del coseno se aplica para la luz emisora difusa superficial= . Al emisor puntual que flota en el espacio se aplica el c=C3=B3digo del sl= ide 12. Pero recomiento usar algo con quasinumbers, para que tenga una dist= ribuci=C3=B3n m=C3=A1s "pareja",=C2=A0sin huecos ni concentracion= es.=C2=A0
Pens=C3=A9 que en el caso de ustedes era un emisor difu= so de superficie, por lo que se ve reflejado en la esfera espejada.=C2=A0No entiendo la forma que tiene esa distribuci=C3=B3n que=C2=A0es=C2=A0c= omo=C2=A0una semiesfera pero con puntas.
=C2=A0
E= l c=C3=B3digo para generar un emisor que siga la ley de coseno, es el del l= ink que les mand=C3=A9 en un mensaje del foro.=C2=A0
El peor caso= es el que les mando ahora.=C2=A0
%% Distribuci=C3=B3n uniforme. La= peor de todas(pero s=C3=B3lo 6 l=C3=ADneas de c=C3=B3digo sin contar lo gr= =C3=A1fico).
figure; hold on
for i=3D1:10000
=C2=A0 =C2=A0rho=3Dsq= rt(rand);
=C2=A0 =C2=A0theta=3Drand*2*pi;
=C2=A0 =C2=A0[x,y]=3Dpol2ca= rt(theta,rho);
=C2=A0 =C2=A0z=3Dsqrt(1-x^2-y^2);
=C2=A0 =C2=A0plot3(x= ,y,z,':');
end
axis('square')

Tambi=C3=A9n les mando una imagen de c=C3=B3mo se genera. Como ven ha= cia arriba se emiten m=C3=A1s fotones, y hacia el lado inferior de la semie= sfera se emiten menos fotones.=C2=A0

saludos,
Eduardo


On Mon, Oct 12, 2020 at 2:55 PM Paula <= paulatavidian@gmail.com> = wrote:
Hola Eduardo,=C2=A0
muchas gracias por la respuesta, nos aclar= =C3=B3 bastante y luego estaremos probando las distintas formas de tratar l= a luz y el color de los fotones para ver cu=C3=A1l es la m=C3=A1s adecuada = para el caso. Por otro lado, no tenemos problema que se publiquen en el for= o las dudas.

Respecto a las direcciones de la emis= i=C3=B3n de fotones, justo est=C3=A1bamos probando eso y ahora nos surgi=C3= =B3 la duda, =C2=BFdesde el punto de la luz tienen que ser emitidos con la = ley del coseno? Porque nosotros est=C3=A1bamos aplicando (o al menos intent= ando) la ley del coseno para el caso que un fot=C3=B3n en la ruleta rusa en= tre en el caso de difusi=C3=B3n. Para el caso de la luz (que por el momento= es =C3=BAnicamente un punto y no un =C3=A1rea), est=C3=A1bamos emitiendo l= as direcciones con n=C3=BAmeros=C2=A0quasi-random y en la semiesfera que da= al cuarto. Otra aclaraci=C3=B3n es que en la imagen,=C2=A0 la ubicaci=C3= =B3n de la luz en este caso no est=C3=A1 en el centro del cuarto sino que u= n poco por encima de la c=C3=A1mara.

Por otro lado= , est=C3=A1bamos viendo si la forma que aplicamos la ley del coseno estaba = correcta. Intentamos replicar en python el c=C3=B3digo del eva para la ley = del coseno y obtuvimos el siguiente resultado:
3D"image.png"
<= /div>
esta ser=C3=ADa la forma del cono? Nos imaginamos que iba a tener= una forma distinta, m=C3=A1s parecida a un cono o un globo. Si esta es la = forma, d=C3=B3nde estar=C3=ADa el origen de la emisi=C3=B3n?

=
Nuevamente muchas gracias!


El lun., 12 de oc= t. de 2020 a la(s) 12:47, Eduardo Fern=C3=A1ndez (edufer111@gmail.com) escribi=C3=B3:
=
Un= =C3=BAltimo comentario sobre las im=C3=A1genes. Quiz=C3=A1 es una ilusi=C3= =B3n, pero me parece que el emisor no emite seg=C3=BAn la ley del coseno. V= eo que las paredes est=C3=A1n muy iluminadas contra el techo, que le llega = igual cantidad de fotones en toda su superficie. Quiz=C3=A1 es s=C3=B3lo un= a impresi=C3=B3n.
Eduardo

On Mon, Oct 12, 2020 at 11:32 AM Eduardo= Fern=C3=A1ndez <edufer111@gmail.com> wrote:
Hola Paula y Leonard= o,

On Sun, Oct 11, 2020 at 9:31 PM Paula <paulatavidian@gmail.com> wrote:
Buena= s noches,
esperamos no molestar debido al d=C3=ADa y hora pero tenemos u= na duda y nos gustar=C3=ADa plantearla, si no nos pueden responder antes de= la clase no hay problema lo vemos ah=C3=AD.
Estuvimos probando cosas pe= ro no logramos entender del todo el manejo de potencia, colores y coeficien= tes difusos. Esto ser=C3=ADa para luces, fotones y superficies. (en los sig= uientes p=C3=A1rrafos, cuando decimos que algo tiene color, nos referimos a= un vector3 rgb con valores de 0 a 1.)

Estuve pensando y el tema de la potencia (dividir la potencia total p= or los fotones, etc.) en realidad es algo confuso y que no es =C3=BAtil. Je= nsen nos hace confundir con esas explicaciones, de dividir la potencia en l= os fotones. Lo que importa es la relaci=C3=B3n entre las luces de las super= ficies. Todos sabemos que si una foto sale oscura, con una c=C3=A1mara m=C3= =A1s sensible saldr=C3=A1 m=C3=A1s brillante (o con m=C3=A1s tiempo de expo= sici=C3=B3n). Y lo que queremos siempre es ver bien la imagen. En nuestro c= aso, si vemos una foto oscura o brillante, la podemos "arreglar" = multiplicando los p=C3=ADxeles por la constante adecuada, o por la funci=C3= =B3n adecuada,=C2=A0para lograr ver la imagen claramente.
=C2=A0<= /div>
Lo que importa es que si tengo dos l=C3=A1mparas, por ejemplo una= con 100W y otra con 50W, entonces la primera emite el doble de fotones que= la segunda. En ambas l=C3=A1mparas, los fotones emitidos tienen la misma p= otencia. Lo que define la potencia de cada l=C3=A1mpara es la cantidad de f= otones emitidos por cada una. Luego, cuando se tiene el mapa de fotones y s= e va a generar la imagen, entonces lo que importa, lo que define la intensi= dad de la luz en las superficies es la cantidad de fotones por unidad de = =C3=A1rea. Si en la superficie B hay 1 fot=C3=B3n por unidad de =C3=A1rea y= en la superficie C hay 10 fotones por unidad de =C3=A1rea, entonces C debe= lucir 10 veces m=C3=A1s brillante que B. Nuestro algoritmo har=C3=A1 los a= justes pertinentes para que la imagen salga n=C3=ADtida.=C2=A0 =C2=A0 =C2= =A0
=C2=A0
Luces: En primer lugar, lo que estamos haciend= o es dividir la potencia de la luz entre la cantidad de fotones y llamamos = a la funci=C3=B3n recursiva que emite y almacena los fotones con el resulta= do de la divisi=C3=B3n guardado en un vec3. Por ahora ponemos la misma pote= ncia para cada color ya que estamos probando pero no tenemos claro que si q= ueremos que la luz tenga cierto color qu=C3=A9 es lo que debemos hacer (cap= az que tener un color para la luz y ponderarlo por la potencia, o tener pot= encia distinta para cada color?).
=C2=A0
Cuando la luz es solo potencia, sin color, los fotones claramente mantie= nen la misma potencia en cada "rebote".
Yo probar=C3=AD= a poni=C3=A9ndole a cada fot=C3=B3n el color (1,1,1) cuando la luz emitida = es blanca y el (r,g,b) adecuado entre 0 y 1 cuando tiene color. Si la luz e= s roja, entonces el color ser=C3=ADa (1,0,0) y ver=C3=ADa el efecto que gen= era. Si hay una l=C3=A1mpara B de luz Blanca con 100W y una l=C3=A1mpara R = de 50W con luz roja, y el total de fotones es 15000, entonces B=C2=A0emitir= =C3=ADa=C2=A010000 fotones con color (1,1,1) y R emitir=C3=ADa 5000 fotones= con color (1,0,0). Se puede afinar m=C3=A1s (por ejemplo que el m=C3=B3dul= o o norma del vector color sea siempre 1, cosa que los fotones tengan la mi= sma "potencia", y por tanto los fotones blancos deber=C3=ADan ten= er valores [sqrt(1/3), sqrt(1/3), sqrt(1/3)] ) pero me parece que para una primera aproximaci=C3=B3n est=C3= =A1 m=C3=A1s que bien.=C2=A0
=C2=A0
Fotones: En las diapositi= vas dice que la potencia es un char de 4 valores pero en la clase dijeron q= ue eso se pod=C3=ADa usar con tres valores o como nos quede m=C3=A1s c=C3= =B3modo. En este caso entonces la potencia equivale al color del fot=C3=B3n= y no se deber=C3=ADa tener nada m=C3=A1s? Es decir, un vec3 con un valor p= ara cada color entre 0 y 1. Como este color va cambiando cu=C3=A1ndo un fot= on "rebota" (entendemos que no es que rebote sino que ser=C3=ADa = un fot=C3=B3n nuevo) =C2=A0debido al sangrado no entendemos como se puede r= espetar "que todos los fotones tengan la misma potencia" o quizas= se refiere =C3=BAnicamente a los emitidos inicialmente por la luz.
=C2=A0
Cuando las paredes tienen color, y se gene= ra el cambio de color de los fotones que "rebotan", la cuenta que= se hace es la especificada en los slides 28 y 29. Sobre si mantiene o no l= a misma potencia, la respuesta es NO, si se hacen las cuentas de los slides= 28 y 29.=C2=A0=C2=A0
Para mi la cuenta adecuada, que mantendr=C3= =ADa la potencia de cada fot=C3=B3n luego del rebote deber=C3=ADa ser:=C2= =A0

Pinc=3D(Pr,Pg,Pb), power of the incident photo= n
S=3D(Sr,Sg,Sb), specular reflectance
D=3D(Dr,Dg,Db), = diffuse reflectance
then
Ps=3D||(SrPr,SgPg,SbPb)||/||Pi= nc||=C2=A0 where || || is the 2-norm and Ps is the probability of specular = reflection
Pd=3D||(DrPr,DgPg,DbPb)||/||Pinc||=C2=A0 =C2=A0where P= d is the probability of diffuse reflection
and also
=
Prefl,s=3D(SrPr,SgPg,SbPb)/Ps=C2=A0 power of reflected specular photon=
Prefl,d=3D(DrPr,DgPg,DbPb)/Pd=C2=A0 power of reflected diffu= se photon=C2=A0

Est=C3=A1 en ingl=C3=A9s porque lo= saqu=C3=A9 de un mail que le mand=C3=A9 a Jensen y que todav=C3=ADa espero= respuesta :-).=C2=A0

Si tienen ganas podr=C3=ADan= probar mi cuenta y la de Jensen y comparar diferencias (yo no la prob=C3= =A9 en un algoritmo de PM). Hay un peque=C3=B1o cambio en el c=C3=A1lculo d= e Ps y Pd, y mi pregunta es por qu=C3=A9 Jensen usa max (norma infinito) en= lugar de norma 2. Sospecho que es para hacer cuentas m=C3=A1s r=C3=A1pidas= y no usar raiz cuadrada. Y quiz=C3=A1 ambas aproximaciones convergen a la = misma imagen (es lo que no s=C3=A9 y me gustar=C3=ADa probar). Pero sospech= o que usar norma 2 es m=C3=A1s eficiente en cuanto a almacenamiento porque = evita la posibilidad de guardar fotones con muy poca energ=C3=ADa, fotones = que influyen poco en el resultado final.=C2=A0
=C2=A0
Superficies= : finalmente, en este caso es el que posiblemente tenemos m=C3=A1s duda= s de c=C3=B3mo implementarlo. Entendemos que se tiene un kdr, kdg y kdb (lo= mismo con especular). Estos coeficientes, que ser=C3=ADan exactamente? Por= que a cada superficie(o mejor dicho cada primitiva) le estamos asignando un= color ( vec3 de 0 a 1). No entendemos cu=C3=A1l ser=C3=ADa la diferencia o= relaci=C3=B3n entre el color y los kd para cada color. O mejor dicho, este= "color" que le estamos asignando a la superficie ya representa l= os kd para cada color?

No entend= =C3=AD por qu=C3=A9 ponen la letra k delante. En los slides del curso es (d= r,dg,db). Pero S=C3=8D, el color de la superficie es el (dr,dg,db).
=C2=A0
Tenemos m=C3=A1s dudas pero esta es una que nos aclarar=C3=ADa bas= tante y ya podr=C3=ADamos emprolijarlo en el c=C3=B3digo ya que estuvimos m= edio que usando el color como el kd para cada componente.. =C2=A0
<= br>
Adjuntamos tambi=C3=A9n un par de im=C3=A1genes para que vean= como estamos emitiendo los fotones. La primera es del mapa de fotones(2000= 00) y la segunda es el resultado de ese mapa en la imagen. (Probablemente a= greguemos algo de fatt en el algoritmo de Ray Tracing ya que se nos est=C3= =A1n quemando un poco los objetos muy cercanos a la luz)=C2=A0
3D"image.png"

3D"image.png"

=C2=A0 Muchas gracias! Nos vemos ma=C3=B1ana en la = consulta.=C2=A0=C2=A0

Muy b= uenas las im=C3=A1genes. Se nota que hay un poco de sangrado, si se notase = m=C3=A1s ser=C3=ADa=C2=A0mejor.=C2=A0
Nos vemos hoy.=C2=A0
<= div>
saludos
Eduardo

ps. = =C2=BFLes parece bien mandar el mail de ustedes y mi respuesta al foro del = curso? As=C3=AD todos manejamos los mismos conceptos. La idea es que todos = aprendamos de todos.=C2=A0


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