From 797deafaebf50228e3479da0d214c5a3d7720772 Mon Sep 17 00:00:00 2001 From: Wenzel Jakob Date: Mon, 25 May 2015 14:15:15 +0200 Subject: [PATCH] Specular motion vector integrator --- doc/images/integrator_motion_path_d.jpg | Bin 0 -> 29583 bytes doc/images/integrator_motion_path_rd.jpg | Bin 0 -> 44841 bytes doc/images/integrator_motion_path_trrtd.jpg | Bin 0 -> 61780 bytes doc/images/integrator_motion_path_trtd.jpg | Bin 0 -> 66612 bytes doc/images/integrator_motion_path_ttd.jpg | Bin 0 -> 40020 bytes doc/images/integrator_motion_sphere_1.jpg | Bin 0 -> 205799 bytes doc/images/integrator_motion_sphere_2.jpg | Bin 0 -> 203825 bytes src/integrators/SConscript | 1 + src/integrators/misc/motion.cpp | 563 ++++++++++++++++++++ 9 files changed, 564 insertions(+) create mode 100644 doc/images/integrator_motion_path_d.jpg create mode 100644 doc/images/integrator_motion_path_rd.jpg create mode 100644 doc/images/integrator_motion_path_trrtd.jpg create mode 100644 doc/images/integrator_motion_path_trtd.jpg create mode 100644 doc/images/integrator_motion_path_ttd.jpg create mode 100644 doc/images/integrator_motion_sphere_1.jpg create mode 100644 doc/images/integrator_motion_sphere_2.jpg create mode 100644 src/integrators/misc/motion.cpp diff --git a/doc/images/integrator_motion_path_d.jpg b/doc/images/integrator_motion_path_d.jpg new file mode 100644 index 0000000000000000000000000000000000000000..8f06a9f638c857326c6cd7ae8c2b57eeaf5f200e GIT binary patch literal 29583 zcmeFZ2Ut_v+Af;4EGQO4L8M5QBGLpbbb)MT0|G*%cd`%>0U;nDov1YFDotsT5<&0{!+I2=p894PuXiG=Sg!&%Smm`9G@xIGg!nM1Po*m{q&3A@hK=h)RxP+vfyn>>V zvWmvvHMO*F>F64pn3|beSXw#UbG+~Lz}dyi+vl;bpMOATSa?L_^Qh=oiAl*RsjuIp z<>cm}^3esD!uMt6_=?J^57muL%`L5MpFX$u68riG28V`6NRv}Pre|j7$n&df>l>TY zE!sAHw_U%1_Wh&Fem3kswTl~Q*YErH@7vF@+pgb!_XW0n-1`rlyK?a44MPrl&r|2G zK0U;9^JR8v!(owYMikz=k9s&yUyvh-uI@H%uVw#h4SV*#)v|vy?BCio0y?_yH(>Dg zaf2WrHV8r&&w0Z6|8M`_=mW`)VLNRnctIVi*Llm_{IOZ(3S4sd+nDpJB^2Qd_r7yO zzCTGIB~$);t$XjNW`U*7)$_K0yN74S6fv=jkYN?%D54BfQQt;Ag2N*mfbT|4W-%2Z z)y4Y428AJ5Vg&dw6}AYcrTG)?GMV=mjC3l^(sWD{-92@*Vn0af)XZUY3i{!?j~-`c zMc#X~*!U>y+|yQFAIU!ph+!W6(-Qq($ST`z;+i);n0yh}GJSVPr-M&d26e#b@TV_1 z(NY?*;yKZv|JQA}2Q>JOdXNS?v@T45`ER{#r}%my=e4ABx>(nZMC|b`JP)X+LY+nbg8#Xiere9f7%I^OFzk zc!fjKg=GKi9WC@ryu<45vzwV8G^^|nf>3|Nx44&E`}Ho5tgMeotZF}_Y4+#7x!<>{ zL^trrGEH7{C_7{l=AS9Kk!>XB;RCMD74iv^{+2_Wu1%$apN#*F4aytrJ+CCx_Kcz4 zdaqVA0Ugl!nV zZEk17m0bT@oNd%Ghc4(;(%N6Diyj^P=Y^D(VJ>spLjcd>sCbT*s_#4 ztB*C><6|qVrroqQ?s^(rZlxZR>*uRq(Zhh`k<(7UbeauL)a_Z6_U=>|Tsqa^<4JWD z6n~2k?XJ#peN$VI+L`5iKe+eSqW8k~jw)Tp$uEpdVQD<+5D9qcm(f~h)6FgJ6*7-f zG0AVdqSZuMH z3|_8^7^L`C6Fp`#TvYk;!QhF7fJ_$ZKyu&LV~{(2OW-DYm{~7==A~<(chtd3u^!fO z=1cW`G{}w$g7$X^NuqCKr2^4RY*ido86T}5q~@_fQSsr`gN=$X$I9v*H8jIG>IXAx zV11@pz9ie`v$h97G3pg+IH*%tmJ@z1&^vs2qsjCDv+oi`@HhPxK z@7yYoED7mKPuSXug#4{L2ON%naJLHfvE)eej8Z_-Dvy`J5P6)<~?qJh9FnZlSo^ordadQD?F}V-!$d^O`qpXHy zrUq9e+q9nn1MMpYBJP4vdvV0P5g(L+N`?+1Fv#5d+}2`%?OWGTzX zeJQ22T$~n-ZoPZuaJx|~>LS)8&D|*W-e`aO6}U;l++yUDD#38a!<4pz9?0VcnJV6x z?sKGXNU>xU6K9jAUesYnn(Fm%6%)z+Tmx>G%P1q166$dKB><0}&>M@tCue1!yn%3b z4czZ*W{x@bz1IAS=uEmlynsCDEc9uv(kdj|)fM6B0ZJKI8yTDDi1%~wS-(F16n0?q z$n~1TES@0M_#>m%F*;ctjRL3B{a)HMQ$A7C;xipw3!JxflMcHEbstCVc z%}p1n%ENDFEQ49uuN^$hGh85rcNa)FrO_1lP+$10pp2!OX>yu6?75%FGg?h5)0K3b zZ!+Yzn#~2sfKaGJ*N4l=D@&9fR&V27e~--)W-+gekIeSuau9qHKIAo#g+tA!j2x@4 zA*mV7lW}sLMnsGH{+!-7-r?^;ZwFtu%p%JlJB;5iFui#7TMG{AFWrJdM#(Kn7caWi zd#-{Rr$$@N2o69%(3=ED_yBLD zDo`chnK{t+EUY2yt)uW|T1?`ITvfuU_}ma@!%p(oPUR8w;$)T>zd^nNrwTMBMKZ(D zNOhBEJ0Hb}nFKFR&;|VBXJKb2>a`n(L-R3)UsP3F?`Ir(*W=e8TS$6ES-y6l=}dGo z&X{w4YVDGv)fvf>h~s{6hwv0IC2^8t@xy95slT`)yO8Fv<6uzJN9viZqu@UdmSSM8 ziq#4UZldAuWpH5XVhUAJz@`&@2)q-h(d&*XUlsi}a<;PDlzG|w*yMNwj7!yjmJl1n zOG0wnLi2TU*&t_^0JS7~XGOZ~2z0od3IA*hyS;X=wz{f3-JlMi)jsbpvn2X#Zo8je z$;G_j`63$C{NaF*v9a6Kqkxqo@&}i5C}&VsykfjQU8Q}e45PhA-JK}1F|bm_$SeKx zGs1^xb+0{`5NvO(l2h};eB~w1*9A=}s0W_+H7=F$K5Obra*)NEkb-*ioQ(2vW8##E zZwZ;vQXA=$D~p1DvKRYV$6U;c(fAUKzYht*^xOv1?&7h0gK1x3op|ln5SI8}Q6m59uh%VY>3p&l~%Qcf8Tf)M>zgrz+#e|Be9H$6I80twNq$yIm7Wd6Um4 z-n80kZIJKWz+WPJHWC-}u}OMTfM+T)^R^xM$aBomi!x_aTVo6Qb7LCpOHU+=HW_O2 zQpMK)G}Pn){Xe&bJPGMygG!TUW6r}*2i+|l3{uW%^AT_sKJJsMIfzdwtBW18@p~%c z)|#FBz&P(3nKE*-LV%iA)`1zZo1;FayNy+@2N}0~0CPAdc3%5t)zm`}XT^pem=3wYZHBo`XzXACZd>|+WujOn*l>%mVLlBD@Jt@p{bX3lAMQN|oi zweqQ=hPB;M*N_fY5$2(ZXh{o4@xGRsGbOiATZgwgxDcDVe}E$ioFRWOOl$ids_r9U zaVMa8BQ3rd698+cu z@B`ipvRvP8JtWa_P3rt#gU-Gshn%6brn=@nP?0Yj0WP2OF8WZYT>SEyT;jLyHr*F0 z%_}R7I{guW@-0hCEiK=hiRw!TAX$7fEZ~D(J!tu? 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zc9)PgASj@mIAw4H7a~PgP`QnaTjcW6L__B)uJar~seln9f|T6LzE>c~Kmg=?{!SV} z6G)~orJf{6pJIZ;r+dQmEDv(}*3`IeV$$u!_yo8lEbd~S6zb#XDwwiu!&g97} zdM#J2x3%`S;j=zN13N;83PHzE!Ll3Y05pJ;y_kn}$X&p)HVj}c?1tNs(ZM)ks)b53 zI=N$!u}g5=GO!SNprafTUBMxKSimRcaURg@spX@n8IbvesNCU30ui*RA0}9Up~HNU z?POiyNiVP&8|64t!h_F!J9f68mc6|6AzP#W0D-c;-fr7ly~cs&ksA%CZyR>wfS4P^ zg>k!dd@%&!KxP38nUiyQlB&Mu+_Fb>tT{Nyi}!fOHkIVA3w*@VB9&yo#^0PAs(j3# z?(381|d$>&g5nwC;>|nS#ZaaMJr!TdOp5imHvBm V)uz`(_S0?oZ2t7FwBGw||Jmwn8;bw{ literal 0 HcmV?d00001 diff --git a/src/integrators/SConscript b/src/integrators/SConscript index 27eefad8..08933d68 100644 --- a/src/integrators/SConscript +++ b/src/integrators/SConscript @@ -18,6 +18,7 @@ plugins += env.SharedLibrary('adaptive', ['misc/adaptive.cpp']) plugins += env.SharedLibrary('irrcache', ['misc/irrcache.cpp', 'misc/irrcache_proc.cpp']) plugins += env.SharedLibrary('multichannel', ['misc/multichannel.cpp']) plugins += env.SharedLibrary('field', ['misc/field.cpp']) +plugins += env.SharedLibrary('motion', ['misc/motion.cpp']) # Bidirectional techniques bidirEnv = env.Clone() diff --git a/src/integrators/misc/motion.cpp b/src/integrators/misc/motion.cpp new file mode 100644 index 00000000..b10e215a --- /dev/null +++ b/src/integrators/misc/motion.cpp @@ -0,0 +1,563 @@ +/* + This file is part of Mitsuba, a physically based rendering system. + + Copyright (c) 2007-2012 by Wenzel Jakob and others. + + Mitsuba is free software; you can redistribute it and/or modify + it under the terms of the GNU General Public License Version 3 + as published by the Free Software Foundation. + + Mitsuba is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +#include +#include +#include +#include +#include + +DECLARE_DIFFSCALAR_BASE(); + +MTS_NAMESPACE_BEGIN + +static StatsCounter statsConverged( + " manifold", "Converged manifold walks", EPercentage); + +/*!\plugin{motion}{Motion and specular motion vector integrator} + * \parameters{ + * \parameter{time}{\Float}{ + * Denotes the time stamp of the target frame of the motion vectors. + * The current frame is specified via the sensor's \code{shutterOpen} + * and \code{shutterClose} parameters, which should both be set to + * the same value. \default{0} + * } + * \parameter{time}{\String}{ + * Path configuration of the desired motion vectors: + * \begin{enumerate}[(i)] + * \item \textbf{d}: Primary (non-specular) hit points\vspace{-1mm} + * \item \textbf{rd}: A non-specular surface seen through a specular reflection\vspace{-1mm} + * \item \textbf{ttd}: A non-specular surface seen through a pair of specular refractions\vspace{-1mm} + * \item \textbf{trtd}: A non-specular surface seen through a sequence of refraction, reflection, and refraction events.\vspace{-1mm} + * \end{enumerate} + * etc. + * } + * \parameter{derivativesOnly}{\Boolean}{ + * By default, the Manifold Exploration technique is used to accurately + * solve the underlying specular flow problem. When this parameter is set to \code{true}, + * the nonlinear solver is deactivated, and only first-order extrapolations are provided. + * \default{\code{false}} + * } + * \parameter{glossyThreshold}{\Float}{ + * Threshold on the roughness parameter of reflectance models + * to be classified as specular. + * \default{\texttt{0}, i.e.~only perfectly specular materials are classified as specular} + * } + * \parameter{maxTimeSteps}{\Integer}{ + * Maximum number of temporal sub-steps \default{5} + * } + * \parameter{maxSpaceSteps}{\Integer}{ + * Maximum number of spatial sub-steps \default{10} + * } + * } + * This integrator extracts motion vectors for animated input scenes, alternatively + * at primary hit points or at hit points observed through sequences of reflective + * and refractive objects. The first two color components (R and G) of the resulting + * rendering specify the screen-space motion in 2D pixel coordinates, and the last + * component (B) denotes the change in distance of the observed 3D point to the + * camera position. Sometimes a specular path cannot be tracked from one frame to the other, + * e.g. because it does not exist, or because the solver did not converge. In this case, + * the pixel color is set to infinity. The images on the following page show + * motion vectors obtained for a sphere that is moving from the left to the right. + * + * \renderings{ + * \rendering{Input scene at time $t=0$}{integrator_motion_sphere_1} + * \rendering{Input scene at time $t=1$}{integrator_motion_sphere_2} + * } + * \renderings{ + * \medrendering{\code{config="d"}}{integrator_motion_path_d} + * \medrendering{\code{config="rd"}}{integrator_motion_path_rd} + * \medrendering{\code{config="ttd"}}{integrator_motion_path_ttd} + * } + * \renderings{ + * \rendering{\code{config="trtd"}}{integrator_motion_path_trtd} + * \rendering{\code{config="trrtd"}}{integrator_motion_path_trrtd} + * } + * \clearpage + * + * \begin{xml}[caption={Exemplary scene configuration for computing specular motion vectors}] + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * \end{xml} + */ + +class MotionIntegrator : public SamplingIntegrator { +public: + typedef Eigen::Matrix EMatrix; + typedef Eigen::Matrix EVector; + typedef Eigen::Matrix Gradient; + typedef DScalar1 DScalar; + typedef DScalar::DVector3 DVector; + + MotionIntegrator(const Properties &props) : SamplingIntegrator(props) { + m_time = props.getFloat("time"); + m_config = boost::to_lower_copy(props.getString("config", "d")); + if (m_config.length() == 0) + Log(EError, "Path configuration string must have at least one entry!"); + if (m_config[m_config.length()-1] != 'd') + Log(EError, "Configuration string must end with 'd'!"); + + m_derivativesOnly = props.getBoolean("derivativesOnly", false); + m_maxTimeSteps = props.getInteger("maxTimeSteps", 5); + m_maxSpaceSteps = props.getInteger("maxSpaceSteps", 10); + m_glossyThreshold = props.getFloat("glossyThreshold", 0); + m_subSteps = props.getInteger("subSteps", 1); + } + + MotionIntegrator(Stream *stream, InstanceManager *manager) + : SamplingIntegrator(stream, manager) { + m_time = stream->readFloat(); + m_config = stream->readString(); + m_derivativesOnly = stream->readBool(); + m_maxTimeSteps = stream->readInt(); + m_maxSpaceSteps = stream->readInt(); + m_glossyThreshold = stream->readFloat(); + m_subSteps = stream->readInt(); + } + + void serialize(Stream *stream, InstanceManager *manager) const { + SamplingIntegrator::serialize(stream, manager); + stream->writeFloat(m_time); + stream->writeString(m_config); + stream->writeBool(m_derivativesOnly); + stream->writeInt(m_maxTimeSteps); + stream->writeInt(m_maxSpaceSteps); + stream->writeFloat(m_glossyThreshold); + stream->writeInt(m_subSteps); + } + + Spectrum Li(const RayDifferential &r, RadianceQueryRecord &rRec) const { + const Point2 apertureSample(0.5f); + Point p0, p1; + + if (m_config.length() == 1) { + Intersection &its = rRec.its; + + // compute motion of environment + if (!rRec.rayIntersect(r)) { + BSphere sphere = rRec.scene->getBSphere(); + Float nearT, farT; + sphere.radius = 1e6; + sphere.rayIntersect(r, nearT, farT); + p0 = r(nearT); + } else { + p0 = its.p; + } + + p1 = p0; + + // reproject point according to the motion of the intersected shape + if (its.isValid() && its.instance != NULL) { + Intersection its2(its); + its2.adjustTime(m_time); + p1 = its2.p; + } + } else { + std::vector source, target, temp, temp2; + Ray ray(r); + + /* Trace an initial light path with the given configuration*/ + if (!tracePath(rRec, ray, source)) + return Spectrum(0.0f); + + m_scene = rRec.scene; + p0 = source[1].p; + + int timeIteration = 0; + + Float stepSizeReduction = 1.0f; + while (true) { + if (++timeIteration > m_maxTimeSteps) + return Spectrum(std::numeric_limits::infinity()); + + Float maxStepSize = (m_time-r.time) / m_subSteps; + Float timeStepSize = std::min((Float) 1.0f, maxStepSize / (m_time-source[0].time)); + timeStepSize *= stepSizeReduction; + + /* Compute updated intersection records for time 'm_time' */ + adjustTime(rRec, apertureSample, source, target, timeStepSize); + + if (timeIteration == 1) { + bool moved = false; + for (size_t i=0; i 1e-4f) + moved = true; + + if (!moved) + return Spectrum(0.0f); + + if (m_derivativesOnly) { + p1 = extrapolateTimePoint(source, target); + break; + } else { + statsConverged.incrementBase(); + } + } + + if (!timeStep(rRec, source, target, temp, temp2)) { + stepSizeReduction *= 0.5f; + } else { + p1 = source[1].p; + stepSizeReduction = std::min((Float) 1.0f, stepSizeReduction * 2); + + if (std::abs(source[0].time-m_time) < 1e-5f) { + ++statsConverged; + break; + } + } + } + } + + const Sensor *sensor = rRec.scene->getSensor(); + DirectSamplingRecord dRec0(p0, r.time), dRec1(p1, m_time); + sensor->sampleDirect(dRec0, apertureSample); + sensor->sampleDirect(dRec1, apertureSample); + + /* Step 4: Compute depth difference */ + Float dDelta = dRec1.dist - dRec0.dist; + Spectrum result(0.0f); + result.fromLinearRGB(dRec1.uv.x-dRec0.uv.x, + dRec1.uv.y-dRec0.uv.y, + std::isfinite(dDelta) ? dDelta : (Float) 0); + return result; + } + + bool timeStep(RadianceQueryRecord &rRec, std::vector &source, const std::vector &target, std::vector &temp, std::vector &temp2) const { + Ray ray = extrapolateTimeRay(source, target); + + if (!tracePath(rRec, ray, temp)) + return false; + + Float error = computeError(temp, target); + + Float spaceStepSize = 1.0f; + int spaceIteration = 0; + while (error > 1e-5f) { + ++spaceIteration; + + if (spaceIteration > m_maxSpaceSteps) { + return false; + } + + Ray candidateRay = extrapolateSpaceRay(temp, target, spaceStepSize); + + Float candidateError = 0; + if (!tracePath(rRec, candidateRay, temp2)) + candidateError = std::numeric_limits::infinity(); + else + candidateError = computeError(temp2, target); + + if (candidateError < error) { + temp = temp2; + error = candidateError; + spaceStepSize = std::min((Float) 1.0f, spaceStepSize * 2); + } else { + spaceStepSize *= 0.5f; + } + } + + source = temp; + return true; + } + + bool tracePath(RadianceQueryRecord &rRec, Ray ray, std::vector &intersections) const { + int depth = 0; + + Intersection its; + memset(&its, 0, sizeof(Intersection)); + its.p = ray.o; + its.time = ray.time; + + intersections.clear(); + intersections.push_back(its); + + while (depth < (int) m_config.size()) { + rRec.scene->rayIntersect(ray, its); + + char interactionType = m_config[depth++]; + if (interactionType == 'd') { + if (!its.isValid()) { + BSphere sphere = rRec.scene->getBSphere(); + Float nearT, farT; + sphere.radius *= 1000; + bool success = sphere.rayIntersect(ray, nearT, farT); + Assert(success && nearT < 0 && farT > 0); + its.p = ray(farT); + its.geoFrame = its.shFrame = Frame(-ray.d); + its.dpdu = its.geoFrame.s; + its.dpdv = its.geoFrame.t; + its.time = ray.time; + its.uv = Point2(0.0f); + its.shape = its.instance = NULL; + } + + if (its.isValid() && !(its.shape->getBSDF()->getType() & BSDF::EDiffuseReflection) && !its.isEmitter()) + return false; + + intersections.push_back(its); + + break; + } + + if (!its.isValid()) + return false; + + intersections.push_back(its); + + /* Sample BSDF * cos(theta) */ + const BSDF *bsdf = its.shape->getBSDF(); + + BSDFSamplingRecord bRec(its, rRec.sampler, ERadiance); + + if (interactionType == 'r') { + if (bsdf->getType() & BSDF::EDeltaReflection) { + bRec.typeMask = BSDF::EDeltaReflection; + } else if (bsdf->getType() & BSDF::EGlossyReflection) { + for (int i=0; igetComponentCount(); ++i) + if ((bsdf->getType(i) & BSDF::EGlossyReflection) && bsdf->getRoughness(its, i) < m_glossyThreshold) + bRec.typeMask = BSDF::EGlossyReflection; + } + } else if (interactionType == 't') { + if (bsdf->getType() & BSDF::EDeltaTransmission) { + bRec.typeMask = BSDF::EDeltaTransmission; + } else if (bsdf->getType() & BSDF::EGlossyTransmission) { + for (int i=0; igetComponentCount(); ++i) + if ((bsdf->getType(i) & BSDF::EGlossyTransmission) && bsdf->getRoughness(its, i) < m_glossyThreshold) + bRec.typeMask = BSDF::EGlossyTransmission; + } + } + + if (bRec.typeMask == BSDF::EAll) + return false; + + Spectrum bsdfWeight = bsdf->sample(bRec, Point2(0.0f)); + if (bsdfWeight.isZero()) + return false; + + const Vector wo = its.toWorld(bRec.wo); + + ray = Ray(its.p, wo, ray.time); + } + + return true; + } + + void adjustTime(const RadianceQueryRecord &rRec, const Point2 &apertureSample, const std::vector &source, std::vector &target, Float timeStepSize) const { + target = source; + + Float targetTime = (1-timeStepSize) * source[0].time + timeStepSize * m_time; + + const Sensor *sensor = rRec.scene->getSensor(); + DirectSamplingRecord dRec0(Point(0.0f), source[0].time), + dRec1(Point(0.0f), targetTime); + sensor->sampleDirect(dRec0, apertureSample); + sensor->sampleDirect(dRec1, apertureSample); + Assert((source[0].p-dRec0.p).lengthSquared() < 1e-6); + + target[0].p = dRec1.p; + target[0].time = targetTime; + + for (size_t i=1; i &source, const std::vector &target, int i, int rel) const { + DScalar u(rel*2, 0), v(rel*2+1, 0), time(6, 0); + + return DScalar::vector(source[i].p) + + DScalar::vector(source[i].dpdu) * u + + DScalar::vector(source[i].dpdv) * v + + DScalar::vector(target[i].p-source[i].p) * time; + } + + void getVertexFrame(const std::vector &source, const std::vector &target, int i, DVector &s, DVector &t, DVector &n) const { + DScalar u(2, 0), v(3, 0), time(6, 0); + const BSDF *bsdf = source[i].shape->getBSDF(); + + Frame frame, du, dv; + frame = bsdf->getFrame(source[i]); + bsdf->getFrameDerivative(source[i], du, dv); + + DVector n0 = DScalar::vector(frame.n) + + DScalar::vector(du.n) * u + + DScalar::vector(dv.n) * v; + DVector s0 = DScalar::vector(frame.s) + + DScalar::vector(du.s) * u + + DScalar::vector(dv.s) * v; + DVector t0 = DScalar::vector(frame.t) + + DScalar::vector(du.t) * u + + DScalar::vector(dv.t) * v; + + frame = bsdf->getFrame(target[i]); + bsdf->getFrameDerivative(target[i], du, dv); + + DVector n1 = DScalar::vector(frame.n) + + DScalar::vector(du.n) * u + + DScalar::vector(dv.n) * v; + DVector s1 = DScalar::vector(frame.s) + + DScalar::vector(du.s) * u + + DScalar::vector(dv.s) * v; + DVector t1 = DScalar::vector(frame.t) + + DScalar::vector(du.t) * u + + DScalar::vector(dv.t) * v; + + n = (1-time)*n0 + time*n1; + s = (1-time)*s0 + time*s1; + t = (1-time)*t0 + time*t1; + } + + void assembleMatrix(const std::vector &source, const std::vector &target, EMatrix &M) const { + DScalar::setVariableCount(7); + M.resize(2*(source.size()-2), 2*source.size()+1); + M.setZero(); + + for (int i=1; i < (int) source.size()-1; ++i) { + DVector p_pred = getVertexPosition(source, target, i-1, 0); + DVector p_cur = getVertexPosition(source, target, i, 1); + DVector p_succ = getVertexPosition(source, target, i+1, 2); + + DVector s, t, n; + getVertexFrame(source, target, i, s, t, n); + + DVector wi = p_pred - p_cur, wo = p_succ - p_cur; + wi *= inverse(sqrt(wi.dot(wi))); + wo *= inverse(sqrt(wo.dot(wo))); + + Float eta = source[i].shape->getBSDF()->getEta(); + + if (m_config[i-1] == 'r') + eta = 1; + else if (wi.dot(n).getValue() < 0) + eta = 1/eta; + + DVector H = wi + wo * DScalar(eta); + H *= inverse(sqrt(H.dot(H))); + + Gradient H_s = H.dot(s).getGradient(), + H_t = H.dot(t).getGradient(); + + M.block<1, 6>((i-1)*2+0, (i-1)*2) = H_s.segment<6>(0); + M.block<1, 6>((i-1)*2+1, (i-1)*2) = H_t.segment<6>(0); + M((i-1)*2+0, M.cols()-1) = H_s(6); + M((i-1)*2+1, M.cols()-1) = H_t(6); + } + } + + Point extrapolateTimePoint(const std::vector &source, const std::vector &target) const { + EMatrix M; + assembleMatrix(source, target, M); + EVector b = -M.block(0, 2, (source.size()-2)*2, (source.size()-2)*2).lu().solve(M.col(M.cols()-1)); + return target[1].p + target[1].dpdu * b[0] + target[1].dpdv * b[1]; + } + + Ray extrapolateTimeRay(const std::vector &source, const std::vector &target) const { + EMatrix M; + assembleMatrix(source, target, M); + + EVector b = -M.block(0, 2, (source.size()-2)*2, (source.size()-2)*2).lu().solve(M.col(M.cols()-1)); + Point rayOrigin = target[0].p; + Point rayTarget = target[1].p + target[1].dpdu * b[0] + target[1].dpdv * b[1]; + return Ray(rayOrigin, normalize(rayTarget-rayOrigin), target[1].time); + } + + Float computeError(const std::vector &source, const std::vector &target) const { + int last = source.size()-1; + Float scale = std::max(Epsilon,std::max(std::abs(target[last].p.x), std::max(std::abs(target[last].p.y), std::abs(target[last].p.z)))); + return (target[last].p-source[last].p).length() / scale; + } + + Ray extrapolateSpaceRay(const std::vector &source, const std::vector &target, Float stepSize) const { + EMatrix M; + assembleMatrix(source, target, M); + + Eigen::PartialPivLU lu = M.block(0, 2, (source.size()-2)*2, (source.size()-2)*2).lu(); + + int last = source.size()-1; + Vector rel = target[last].p-source[last].p, + dpdu = source[last].dpdu, + dpdv = source[last].dpdv; + + Float b1 = dot(rel, dpdu), + b2 = dot(rel, dpdv), + a11 = dot(dpdu, dpdu), a12 = dot(dpdu, dpdv), + a22 = dot(dpdv, dpdv), + det = a11 * a22 - a12 * a12; + + Float invDet = 1.0f / det, + du = ( a22 * b1 - a12 * b2) * invDet, + dv = (-a12 * b1 + a11 * b2) * invDet; + + EVector b = -(du*lu.solve(M.col(M.cols()-3)) + dv*lu.solve(M.col(M.cols()-2))); + + Point rayTarget = source[1].p + stepSize * (source[1].dpdu * b[0] + source[1].dpdv * b[1]); + + return Ray(source[0].p, normalize(rayTarget-source[0].p), source[1].time); + } + + std::string toString() const { + return "MotionIntegrator[]"; + } + + MTS_DECLARE_CLASS() +private: + Float m_time; + std::string m_config; + bool m_derivativesOnly; + int m_maxSpaceSteps; + int m_maxTimeSteps; + int m_subSteps; + Float m_glossyThreshold; + mutable const Scene *m_scene; +}; + +MTS_IMPLEMENT_CLASS_S(MotionIntegrator, false, SamplingIntegrator) +MTS_EXPORT_PLUGIN(MotionIntegrator, " motion vector integrator"); +MTS_NAMESPACE_END