From 95581a84b23f58b4fae18d17a482793b65fa3894 Mon Sep 17 00:00:00 2001 From: Andreas Fabri Date: Tue, 28 Apr 2015 16:06:32 +0200 Subject: [PATCH] Explain the plausibility with an image --- ...Advancing_front_surface_reconstruction.txt | 20 ++++++++++++++++++ .../fig/wedges.png | Bin 0 -> 6297 bytes 2 files changed, 20 insertions(+) create mode 100755 Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/fig/wedges.png diff --git a/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/Advancing_front_surface_reconstruction.txt b/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/Advancing_front_surface_reconstruction.txt index b62ee6e532c..f8d39241fd6 100644 --- a/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/Advancing_front_surface_reconstruction.txt +++ b/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/Advancing_front_surface_reconstruction.txt @@ -123,6 +123,20 @@ We define the *plausibility* grade \f$ p(t) \f$ as \f$ 1/r_t \f$, if \f$ \beta_t < \beta \f$, and \f$ -\beta_t \f$ else. The parameter \f$ \beta \f$ can be specified by the user and is set by default to \f$ \pi/6\f$. +Let's have a look at the figure below. +\cgalFigureBegin{figAFSRplausible,wedges.png} +Plausibility. Triangle `t'` and incidident triangles sharing edge `e` seen from the side. +\cgalFigureEnd + + \f$ \alpha_\mathrm{sliver}\f$ corresponds to the red wedge. The algorithm will never select triangle `t1` +even if it is the only candidate triangle. + +\f$\beta\f$ corresponds to the green wedge. If there is a candidate triangle in this zone, +the one with the smallest radius is the most plausible. + +If there is no candidate triangle in the green wedge, the triangle with the smallest +angle between its normal and the normal of `t'` is chosen. In the figure above +this would be triangle `t4`. \subsection AFSR_Boundaries Dealing with Multiple Components, Boundaries and Sharp Edges @@ -152,6 +166,12 @@ such that \f$ p(t) < 0\f$, and \f$ r_t > k r_{t'}\f$ where \f$ t'\f$ is the triangle on the surface incident on \f$ e \f$. The parameter \f$ k \f$ is specified by the user and is set by default to 5. +For the example given in \cgalFigureRef{figAFSRplausible}, we said that if there +was no triangle `t3` in the green wedge, triangle `t4` would be chosen as it has +the smallest angle between its normal and the normal of triangle `t'`. +However, in case its radius was \f$ k \f$ times larger than the radius of triangle `t'`, +triangle `t2` would be chosen, assuming that its radius is not \f$ k \f$ times larger. + Note that this heuristic implies that where the sampling is too sparse with respect to curvature, it must diff --git a/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/fig/wedges.png b/Advancing_front_surface_reconstruction/doc/Advancing_front_surface_reconstruction/fig/wedges.png new file mode 100755 index 0000000000000000000000000000000000000000..b92a29a54a624b1ac47a2915565dd56532053593 GIT binary patch literal 6297 zcmcIpdpMN&+t-?6It`{)2Wvz~#Y9w!8Brl=TI|+VnqsRJQQ4X>^Gt?JDkian%~ZS5 zVIxs0%yG-alNf@9lm*pU-`NPxtqh zxMRELoSBPe>gedq@%Gx}r=v3s13!NHGl0c-)6pdGYg(kAr@K!6E0bO@ARON4yHQ7{ zP%sNSFddAE$Gm=u)X_2e75|ymeu#2fM`wYZ_oj^jr}quC(Jy}25?C?(gfwrn**U`e zW!?wH=F!DbZ=ZVHxZmJHaQ`*rQriKs`8o63Ua^zep}_HJWYchJ*fUj|G;?+2&WxRlboRe# z4`EI_Go8%VxphXS>o%Q0(OGVW>g<>X>z$dYPtyr-L#AE(hDXwwZ}9)>;$~;}DogL~ z4@EO;Q%4mSR?Ynv|NfIvH(mAiTXi#jtpCG!Alpg6+_y$Tc@(kVj65aJ0YN4XMouV; zokOI|q%q%JXXfyGbL{_v`1?A>he_dsQZdcc@v!j#)y)T)cAnMF9{pfF;2dU!>YUxc z9l1qh$*=xi_F+VirB8FS8!T@rYsy(erHQgyVjiyx6+s-W=5yCwCTFy?1E_mmQ`Hq$ zJJ8$sx8_#4l~`SRkTNf%}%-0mVEW#Iozh zZmLony8g%;4;RhY1DJjsbYd{uT#j{joo);ZpJ@D*Ta+$!(R^*VE1h0Sq*YW`KERso zUWu?nPqpVCvZIj>XC3m)LgA;D{(MqPl!Z%9Q)E;~=F~K;O1Yh@k}0cBweRhY5M&&` zp!JSaD!-QZ<^ai8D$)x1O9+(xKL;_A!#?URNNG-80qZSDY!-C#g&~Y^HX0|$jwsi{ z_1RQSf7fqufZmJ1t>68aG~b<~hAG@9QSuGi_o85Z@EQCmnEP`X>7l904G~zNI-bjy zD-x?Xw|uV)2-h@SX^=<^PK4b1@itWUciM&8yIL~p(H+LOmMf%RUdz?Yvi zlNt{Dx6>vKZ&%27mo$?i{|=B^qP2!>*}C7t0?4YWr1?rOTwX=e)=Jm-W=eQ}v*!)^ z@3N}5`r|zWvG}$-AU?(;Ig^JzByza^wScdKK=CseG*9HvZT|Ty-)Lz0IW=U1t31YI zl*eb=RzqUvAc{U1N*vCuwJ=n*b#D_tV%za% zJsuFv=&6d}YL#PqhPcPnGdnjU5orb>JU$sqeAc5^Nt!TFEw+3%838v)JMl!-RKOiG zrsgwsJNQwFoG36e+;y;U*KBAhwyNM`F!RV1jrAi_%nM!OT1ee6C4=1ZEpAB43KqwM zjN{Z{OvIvtAJVu8`*#LT9EC`~SWweUwVeuvyulIuezv%$>iCfhYCjLDrLsz2Q=Kq_ zzG|TAcr}zs;4XlL&GxV$o-%i*e}5D#=R>l8i_S92{505g)eCYQe!_#k{kjIebU$U~=le=i;% zJ=PD;Z{%_(g**MbN#bR$fH*a)xhQdxc%>yi+!_KKD;=lAhrog$bhFSVZBfj1hKC$1 zDB?;dJOwss^J4tfE(Gl{p0MIFjvH)a32+N`^SGzpI5LJFMkFsqiSG-j4%6HFT!!0@`bE?aU{7(%iDL&Usk4EN*YnasXfg06tiD zH)nqxbv%st5V7?z!wr!dLGQl+O_Dt?WsGmp3q`q4#)~?}CZ%U>#&K9=jq;pp?V?54SVdEs8*Wk=YN9*m zv9DA8rLray^dwJsMn>6!X4uv?&*DTqn$DD!kTC*CPX{w+Z&1V?Ds#4|VjLt!UvoU3 zyYR$0Kr-MXR()3V+Y1YHiRNN>@JdAi8LJ{f z<~(5n(!H_2Z*`Zvoo}h0GNmID>y!OwA=BHs;urmIjM-}pu_%3Rv`t)u|GxFk1SrrO z7RL}}e>!v2ccP*TIN4`p*5>Hw`3_@s$W0&wigum>1ulfezq~SSjmQbq3I?}El}o!j z{Lc;^Mp(h{X}?-p{J#EL!%re8zJf(cCRdtv_4R%JQa}EO%u^fvCdXG2FFZ%2Q_?4D zGt9xB8IHfk`fZUssGx%dNniB#b^UPTBnM_}LPjmH&sWxiJydoR1dnYPlVn@p^{lUF zU9PRKtLyd^c8be$go^bdT;hb0ro->qz8+H1yNZHrI+{IHD~<^isp2;N+|V9Ggf#Km zWB${n0o*IQzY*K34ucw{<$?Y-~GC@?Xg3dm9o zTgQX@ckFJS@A-}55g7||$VRDwNFBL~s$}^Zf?aax;r1a;+9GU!avvIA7iZi0vgAW^ z;gCk1@Vd!VWq=MEej|0=f9s1Ly;XC6x6|EYF3u6+1#O}2oB~(QP}@?U&EEW((u=*T|aVO3Cr4gSR>Z;8Ai_zPxvTf22n_CUb5|_dek?K*Iwk* zUnhM(WHi=se%ITfH9d1nz9jh|nQn$1+B~M?-NWKAX|V=r%BmA%jf(mMH8UaB1l0Tf zv#CCI`sI@Z@qrAevOfCFjW}_y=J~RA>xC?z?doC+n3=n`imPd&N0_QPs;*>)6P1hf z#)VH`WT9}{HkLbHytTb}E&pqr@Vtz=XM2YjZPA7ga{ILT5(W)R>S`3`=Sw1dF}-cd z+8XEu2q}uFIdF&hma!S>Tg64G*+q0!LDvU5^QxvjFS|)P@$Q~wRY@vWY{Tr2Afsja zngax_*MZMmq4rN%lVt*(BiEKhjcBxCr*AYpRl{^Eg%7d3qT3e%=V_uo#5t6y;EvRF z!4!2+U9v2{4W?KqZk}zQQ96P{(GB5(ogWdF6*k95$(cihLj22n%h^2qP~C)hlQplL zuxX{kalt{t$e!sCnEF*b;W-)E_dCs?ox0RtQ$Mpp@U(P%!`vj!EC2F}rj2sd9teqW zMa%{~4NnnieYvx^te4XM_XE-QJc5M5J<~rdZD7j@=s?sFm&WQDL9lkPp@gTxAlcWGqSjJ5YM{DDc_J zqtoF$f#YITcpn*i2UIj<$iT6bs88d2&DU@W8BUF}Ts(*n7ni=ey0C+^k!h?eUZL>k z?~^UOfcp{?X&&D#()eCymQWSJAUzv$m!fJSHEjoPRvWcB#|~KlzV*T2WzTg~hk>B|F-@X`0u~oR|BK{q4c39FcGe%`tZ+FXTg?)$h&y|OTzNzdc zWq{aJ8BDXK_CP`Ve*R?5%Ecf8eF=Ox)x&}^koC0|b-~R3GB+9Zj=sc`jf2acNDH)= zXPZkOM% zTBN}g7&9l>g0juI5gb?Gw#BCq7p6H;{hE}-zO-B(=)VPrF+U4xjNCRB=+8g{kAGy5=>DraCIO*^HOXv8R)1U? 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