----------------------------
こないだの一連の作業（物体に三角形の網模様を作る＝世間では，メッシュ生成と呼ぶらしい）が滞ってたので，再度ゴソゴソ作業．
とりあえず，小さい目標として
・小さい直方体形状を定義
・三角形のサイズパラメータ
などから，
・triangle コマンドを使い 表面の三角模様埋め（デローニ分割と呼ぶ）
を行い，
・tetgen を使って表面三角形から 内部に四面体敷き詰め（３次元デローニ分割）
をやろうと思う．
中長期的狙いとしては，
直方体底面 には，いくつかの まばらな 矩形領域をつくり，
デローニ分割したい．
----------------------------
《直方体表面に２次元デローニ 三角形を敷き詰める》
以下のようなシェルスクリプトを作る．
#/-----------------------------------------------------------------------
#
# CreateRectangularParallelopipedSTL.sh
# T.Y. Mon. July 23, 2012
#/-----------------------------------------------------------------------
#-------------------------------------------------------
#---------- modify following parameters --------------
#-------------------------------------------------------
####
x0=0.0
y0=0.0
z0=0.0
Lx=100.0
Ly=120.0
Lz=140.0
#dL=5.0
dL=60.0
####
FileBottom="./data/bottom.poly"
FileBottomSTL="./data/bottom.stl"
FileTop="./data/top.poly"
FileTopSTL="./data/top.stl"
FileWest="./data/west.poly"
FileWestSTL="./data/west.stl"
FileEast="./data/east.poly"
FileEastSTL="./data/east.stl"
FileSouth="./data/south.poly"
FileSouthSTL="./data/south.stl"
FileNorth="./data/north.poly"
FileNorthSTL="./data/north.stl"
FileBoxSTL="./data/BOX.stl"
#-------------------------------------------------------
#---------- compile programs -------------------------
#-------------------------------------------------------
gfortran -O2 -Wall -o Shewchuk2STL Shewchuk2STL.f
gfortran -O2 -Wall -o TransformSTL TransformSTL.f
#-------------------------------------------------------
#---------- display parameters -----------------------
#-------------------------------------------------------
echo " "
echo "----------------------------------------"
echo " CreateRectangularParallelopipedSTL.sh "
echo "----------------------------------------"
echo "x0 : "${x0}
echo "y0 : "${y0}
echo "z0 : "${z0}
echo "Lx : "${Lx}
echo "Ly : "${Ly}
echo "Lz : "${Lz}
echo "dL : "${dL}
dS=`echo ${dL} "*" ${dL} "* 0.25 * sqrt(3)"| bc`
echo "dS : "${dS}
echo " "
#-------------------------------------------------------
#---------- bottom STL creation -----------------------
#-------------------------------------------------------
vert01x=${x0}
vert01y=${y0}
vert02x=`echo ${x0}" + "${Lx} | bc`
vert02y=${y0}
vert03x=`echo ${x0}" + "${Lx} | bc`
vert03y=`echo ${y0}" + "${Ly} | bc`
vert04x=${x0}
vert04y=`echo ${y0}" + "${Ly} | bc`
echo "# bottom.poly " > ${FileBottom}
echo "4 2 0 0" >> ${FileBottom}
echo "#">> ${FileBottom}
echo "1 "${vert01x}" "${vert01y} >> ${FileBottom}
echo "2 "${vert02x}" "${vert02y} >> ${FileBottom}
echo "3 "${vert03x}" "${vert03y} >> ${FileBottom}
echo "4 "${vert04x}" "${vert04y} >> ${FileBottom}
echo "#">> ${FileBottom}
echo "4 0" >> ${FileBottom}
echo "1 1 2 ">> ${FileBottom}
echo "2 2 3 ">> ${FileBottom}
echo "3 3 4 ">> ${FileBottom}
echo "4 4 1 ">> ${FileBottom}
echo "#">> ${FileBottom}
echo "0">> ${FileBottom}
triangle -pqa${dS} ${FileBottom}
#triangle -pqa0.01 ${FileBottom}
##---------------------------------
## Shewchuk2STL.f
##---------------------------------
FileCtrl="./Shewchuk2STL.ctl"
echo "############ Shewchuk2STL.ctl" > ${FileCtrl}
echo ${FileBottom%.poly}.1.node >> ${FileCtrl}
echo ${FileBottom%.poly}.1.ele >> ${FileCtrl}
echo ${FileBottom%.poly}.stl >> ${FileCtrl}
echo "" >> ${FileCtrl}
./Shewchuk2STL
#-------------------------------------------------------
#---------- top STL creation -----------------------
#-------------------------------------------------------
##---------------------------------
## TransformSTL.f
##---------------------------------
FileCtrl="./TransformSTL.ctl"
cp ${FileBottomSTL} "./tmp.stl"
echo "#### TransformSTL.ctl #####" > ${FileCtrl}
echo "./tmp.stl" >> ${FileCtrl}
echo ${FileTopSTL} >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "1 0.0 0.0 "`echo ${z0}" + "${Lz} | bc` >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo " " >> ${FileCtrl}
./TransformSTL
rm -f ./tmp.stl
#-------------------------------------------------------
#---------- west STL creation -----------------------
#-------------------------------------------------------
vert01x=${z0}
vert01y=${y0}
vert02x=`echo ${z0}" + "${Lz} | bc`
vert02y=${y0}
vert03x=`echo ${z0}" + "${Lz} | bc`
vert03y=`echo ${y0}" + "${Ly} | bc`
vert04x=${z0}
vert04y=`echo ${y0}" + "${Ly} | bc`
echo "# west.poly " > ${FileWest}
echo "4 2 0 0" >> ${FileWest}
echo "#">> ${FileWest}
echo "1 "${vert01x}" "${vert01y} >> ${FileWest}
echo "2 "${vert02x}" "${vert02y} >> ${FileWest}
echo "3 "${vert03x}" "${vert03y} >> ${FileWest}
echo "4 "${vert04x}" "${vert04y} >> ${FileWest}
echo "#">> ${FileWest}
echo "4 0" >> ${FileWest}
echo "1 1 2 ">> ${FileWest}
echo "2 2 3 ">> ${FileWest}
echo "3 3 4 ">> ${FileWest}
echo "4 4 1 ">> ${FileWest}
echo "#">> ${FileWest}
echo "0">> ${FileWest}
triangle -pqa${dS} ${FileWest}
##---------------------------------
## Shewchuk2STL.f
##---------------------------------
FileCtrl="./Shewchuk2STL.ctl"
echo "############ Shewchuk2STL.ctl" > ${FileCtrl}
echo ${FileWest%.poly}.1.node >> ${FileCtrl}
echo ${FileWest%.poly}.1.ele >> ${FileCtrl}
echo ${FileWest%.poly}.stl >> ${FileCtrl}
echo "" >> ${FileCtrl}
./Shewchuk2STL
##---------------------------------
## TransformSTL.f
##---------------------------------
FileCtrl="./TransformSTL.ctl"
cp ${FileWestSTL} "./tmp.stl"
echo "#### TransformSTL.ctl #####" > ${FileCtrl}
echo "./tmp.stl" >> ${FileCtrl}
echo ${FileWestSTL} >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "1 -90.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo " " >> ${FileCtrl}
./TransformSTL
rm -f ./tmp.stl
#-------------------------------------------------------
#---------- east STL creation -----------------------
#-------------------------------------------------------
##---------------------------------
## TransformSTL.f
##---------------------------------
FileCtrl="./TransformSTL.ctl"
cp ${FileWestSTL} "./tmp.stl"
echo "#### TransformSTL.ctl #####" > ${FileCtrl}
echo "./tmp.stl" >> ${FileCtrl}
echo ${FileEastSTL} >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "1 "`echo ${x0}" + "${Lx} | bc`" 0.0 0.0 " >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo " " >> ${FileCtrl}
./TransformSTL
rm -f ./tmp.stl
#-------------------------------------------------------
#---------- south STL creation -----------------------
#-------------------------------------------------------
vert01x=${x0}
vert01y=${z0}
vert02x=`echo ${x0}" + "${Lx} | bc`
vert02y=${z0}
vert03x=`echo ${x0}" + "${Lx} | bc`
vert03y=`echo ${z0}" + "${Lz} | bc`
vert04x=${x0}
vert04y=`echo ${z0}" + "${Lz} | bc`
echo "# south.poly " > ${FileSouth}
echo "4 2 0 0" >> ${FileSouth}
echo "#">> ${FileSouth}
echo "1 "${vert01x}" "${vert01y} >> ${FileSouth}
echo "2 "${vert02x}" "${vert02y} >> ${FileSouth}
echo "3 "${vert03x}" "${vert03y} >> ${FileSouth}
echo "4 "${vert04x}" "${vert04y} >> ${FileSouth}
echo "#">> ${FileSouth}
echo "4 0" >> ${FileSouth}
echo "1 1 2 ">> ${FileSouth}
echo "2 2 3 ">> ${FileSouth}
echo "3 3 4 ">> ${FileSouth}
echo "4 4 1 ">> ${FileSouth}
echo "#">> ${FileSouth}
echo "0">> ${FileSouth}
triangle -pqa${dS} ${FileSouth}
##---------------------------------
## Shewchuk2STL.f
##---------------------------------
FileCtrl="./Shewchuk2STL.ctl"
echo "############ Shewchuk2STL.ctl" > ${FileCtrl}
echo ${FileSouth%.poly}.1.node >> ${FileCtrl}
echo ${FileSouth%.poly}.1.ele >> ${FileCtrl}
echo ${FileSouth%.poly}.stl >> ${FileCtrl}
echo "" >> ${FileCtrl}
./Shewchuk2STL
##---------------------------------
## TransformSTL.f
##---------------------------------
FileCtrl="./TransformSTL.ctl"
cp ${FileSouthSTL} "./tmp.stl"
echo "#### TransformSTL.ctl #####" > ${FileCtrl}
echo "./tmp.stl" >> ${FileCtrl}
echo ${FileSouthSTL} >> ${FileCtrl}
echo "1 90.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo " " >> ${FileCtrl}
./TransformSTL
rm -f ./tmp.stl
#-------------------------------------------------------
#---------- north STL creation -----------------------
#-------------------------------------------------------
##---------------------------------
## TransformSTL.f
##---------------------------------
FileCtrl="./TransformSTL.ctl"
cp ${FileSouthSTL} "./tmp.stl"
echo "#### TransformSTL.ctl #####" > ${FileCtrl}
echo "./tmp.stl" >> ${FileCtrl}
echo ${FileNorthSTL} >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "0 0.0" >> ${FileCtrl}
echo "1 0.0 "`echo ${y0}" + "${Ly} | bc` " 0.0 " >> ${FileCtrl}
echo "0 0.0 0.0 0.0" >> ${FileCtrl}
echo " " >> ${FileCtrl}
./TransformSTL
rm -f ./tmp.stl
#-------------------------------------------------------
#---------- merge six rectangulars -------------------
#-------------------------------------------------------
cat ${FileBottomSTL} > ${FileBoxSTL}
cat ${FileTopSTL} >> ${FileBoxSTL}
cat ${FileSouthSTL} >> ${FileBoxSTL}
cat ${FileNorthSTL} >> ${FileBoxSTL}
cat ${FileWestSTL} >> ${FileBoxSTL}
cat ${FileEastSTL} >> ${FileBoxSTL}
#-------------------------------------------------------
#---------- single solid STL -------------------------
#-------------------------------------------------------
cp ${FileBoxSTL} "./tmp.stl"
echo "solid BOX" > ${FileBoxSTL}
awk '($1 != "solid" && $1 != "endsolid"){print}' "./tmp.stl" >> ${FileBoxSTL}
#awk '($1 != "solid" ){print}' "./tmp.stl" >> ${FileBoxSTL}
echo "endsolid BOX" >> ${FileBoxSTL}
rm -f "./tmp.stl"
上記のスクリプト内にあるように，途中で２つの Fortran プログラムを使う．
で，処理すると，
こんな感じのものができる．
生成物は STL ファイル（→表示はパラビュー）
----------------------------
《直方体 表面三角形から 内部に四面体敷き詰め》
３次元デローニをつかうために tetgen を使う．
以下のように STL から poly ファイル（tetgen の条件ファイル）を生成するスクリプトを作成．
#!/bin/bash
FileInput=./data/BOX.stl
FileOutput=./data/BOX.poly
#FileInput=./data/box_shape.stl
#FileOutput=./data/box_shape.poly
echo "------------------------------------"
echo "--------- STL2POLY3d.sh -----------"
echo "------------------------------------"
echo ""
date
nStart=`awk '($1 == "solid"){printf("%d\n", NR)}' ${FileInput}`
echo "nStart : "${nStart}
nEnd=`awk '($1 == "endsolid"){printf("%d\n", NR)}' ${FileInput}`
echo "nEnd : "${nEnd}
nRow=`wc -l ${FileInput} | awk '{printf("%d\n", $1)}' `
echo "nRow : "${nRow}
nFacet=`echo " (${nEnd} - ${nStart} - 1) / 7" | bc`
echo "nFacet : "${nFacet}
nNodes=`echo " ${nFacet} * 3" | bc`
echo "nNodes : "${nNodes}
#--------------
echo "# " > ${FileOutput}
echo "# poly data derived from STL file" >> ${FileOutput}
echo "# input: "${FileInput} >> ${FileOutput}
echo "# output: "${FileOutput} >> ${FileOutput}
echo "# " >> ${FileOutput}
echo "# " >> ${FileOutput}
#--------------
echo "# node part" >> ${FileOutput}
echo ${nNodes}" 3 0 0" >> ${FileOutput}
awk '($1 == "vertex"){printf("%15.5f %15.5f %15.5f\n", $2, $3, $4)}' ${FileInput} > "./tmp.vert"
awk '{printf("%5.5d %15.5f %15.5f %15.5f\n",NR, $1, $2, $3)}' "./tmp.vert" >> ${FileOutput}
echo "# " >> ${FileOutput}
echo "# " >> ${FileOutput}
#--------------
echo "# facet part" >> ${FileOutput}
echo ${nFacet}" 1" >> ${FileOutput}
nCount=1
while [ $nCount -le ${nFacet} ] ; do
# echo "Facet Count:"${nCount}
nCount=`expr $nCount + 1`
vert1=`echo "($nCount - 2) * 3 + 1" | bc`
vert2=`echo "($nCount - 2) * 3 + 2" | bc`
vert3=`echo "($nCount - 2) * 3 + 3" | bc`
echo " 1 0 1 " >> ${FileOutput}
echo " 3 "${vert1}" "${vert2}" "${vert3} >> ${FileOutput}
done
echo "# " >> ${FileOutput}
echo "# " >> ${FileOutput}
#--------------
echo "# hole part" >> ${FileOutput}
echo " 0" >> ${FileOutput}
echo "# " >> ${FileOutput}
echo "# " >> ${FileOutput}
#--------------
echo "# region part" >> ${FileOutput}
echo " 0" >> ${FileOutput}
echo "# " >> ${FileOutput}
echo "# " >> ${FileOutput}
date
重複点を許容するという想定で，STL の facet を順次 poly ファイルリストに流し込んでるだけ．
ここから処理をするために，
tetgen -pK ./data/BOX.poly
とやると，以下のようなエラー
............（中略） ...................
Warning: Point #296 is duplicated with Point #275. Ignored!
Warning: Point #90 is duplicated with Point #72. Ignored!
Warning: Point #297 is duplicated with Point #283. Ignored!
Warning: Point #100 is duplicated with Point #72. Ignored!
Warning: Point #98 is duplicated with Point #72. Ignored!
Delaunay seconds: 0
Creating surface mesh.
Recovering boundaries.
Error: Invalid PLC! A point and a segment intersect.
Point: 336. Segment: (62, 334).
Program stopped.
色々とチェックしてわかったが，２次元デローニ処理をするときに
以下のような不整合点をつくってしまうことが判明．
----------------------------
修正目標
CreateRectangularParallelopipedSTL.sh の入力パラメータの
dL を triangle コマンド渡しせずに，
node 点を区切ってしまうことにすると うまく行く？
----------------------------
triangle コマンドをもう一度おさらいすると，
こんなページに行き付き，
"-Y" オプションが有効であることがわかる．
----------------------------
以下，修正版 スクリプト（作りかけ＝bottom 面のみ）
#!/bin/bash
#/-----------------------------------------------------------------------
#
# samp.sh
# T.Y. Fri. July 27, 2012
#/-----------------------------------------------------------------------
#-------------------------------------------------------
#---------- modify following parameters --------------
#-------------------------------------------------------
####
x0=0.0
y0=0.0
z0=0.0
Lx=100.0
Ly=120.0
Lz=140.0
Nx=5
Ny=6
Nz=7
dL=60.0
####
FileBottom="./data/bottom.poly"
FileBottomSTL="./data/bottom.stl"
FileTop="./data/top.poly"
FileTopSTL="./data/top.stl"
FileWest="./data/west.poly"
FileWestSTL="./data/west.stl"
FileEast="./data/east.poly"
FileEastSTL="./data/east.stl"
FileSouth="./data/south.poly"
FileSouthSTL="./data/south.stl"
FileNorth="./data/north.poly"
FileNorthSTL="./data/north.stl"
FileBoxSTL="./data/BOX.stl"
#-------------------------------------------------------
#---------- compile programs -------------------------
#-------------------------------------------------------
gfortran -O2 -Wall -o Shewchuk2STL Shewchuk2STL.f
gfortran -O2 -Wall -o TransformSTL TransformSTL.f
#-------------------------------------------------------
#---------- display parameters -----------------------
#-------------------------------------------------------
echo " "
echo "----------------------------------------"
echo " CreateRectangularParallelopipedSTL.sh "
echo "----------------------------------------"
echo "x0 : "${x0}
echo "y0 : "${y0}
echo "z0 : "${z0}
echo "Lx : "${Lx}
echo "Ly : "${Ly}
echo "Lz : "${Lz}
echo "Nx : "${Nx}
echo "Ny : "${Ny}
echo "Nz : "${Nz}
echo " "
dX=`echo " ${Lx} / ${Nx} "| bc`
dY=`echo " ${Ly} / ${Ny} "| bc`
dZ=`echo " ${Lz} / ${Nz} "| bc`
echo "dX : "${dX}
echo "dY : "${dY}
echo "dZ : "${dZ}
echo " "
#-------------------------------------------------------
#---------- bottom STL creation -----------------------
#-------------------------------------------------------
echo "# bottom.poly " > ${FileBottom}
nNodes=`echo " ( ( ${Nx} + 1 ) * 2 ) + ( ( ${Ny} - 1 ) * 2 ) "| bc`
echo "#-------------------------------">> ${FileBottom}
echo ${nNodes}" 2 0 0" >> ${FileBottom}
echo "#-------------------------------">> ${FileBottom}
nCount=0
#---- lower side ----
LoopCount=0
echo "# lower side" >> ${FileBottom}
while [ $LoopCount -lt ${Nx} ] ; do
nCount=`expr $nCount + 1`
LoopCount=`expr $LoopCount + 1`
echo "Node Count:"${nCount}
xx=`echo " ${x0} + ( ${LoopCount} - 1 ) * ${dX} " | bc`
yy=${y0}
echo ${nCount}" "${xx}" "${yy} >> ${FileBottom}
done
nCount=`expr $nCount + 1`
echo "Node Count:"${nCount}
xx=`echo " ${x0} + ${Lx} " | bc`
echo ${nCount}" "${xx}" "${yy} >> ${FileBottom}
echo "# " >> ${FileBottom}
#---- right side ----
LoopCount=0
echo "# right side" >> ${FileBottom}
while [ $LoopCount -lt ${Ny} ] ; do
nCount=`expr $nCount + 1`
LoopCount=`expr $LoopCount + 1`
echo "Node Count:"${nCount}
xx=`echo " ${x0} + ${Lx} " | bc`
yy=`echo " ${y0} + ( ${LoopCount} ) * ${dY} " | bc`
echo ${nCount}" "${xx}" "${yy} >> ${FileBottom}
done
echo "# " >> ${FileBottom}
#---- upper side ----
LoopCount=0
echo "# upper side" >> ${FileBottom}
while [ $LoopCount -lt ${Nx} ] ; do
nCount=`expr $nCount + 1`
LoopCount=`expr $LoopCount + 1`
echo "Node Count:"${nCount}
xx=`echo " ( ${x0} + ${Lx} ) - ${dX} * ( ${LoopCount} ) " | bc`
yy=`echo " ${y0} + ${Ly} " | bc`
echo ${nCount}" "${xx}" "${yy} >> ${FileBottom}
done
echo "# " >> ${FileBottom}
#---- left side ----
LoopCount=0
echo "# left side" >> ${FileBottom}
Nym1=`expr ${Ny} - 1`
#while [ $LoopCount -lt ${Ny} ] ; do
while [ $LoopCount -lt ${Nym1} ] ; do
nCount=`expr $nCount + 1`
LoopCount=`expr $LoopCount + 1`
echo "Node Count:"${nCount}
xx=${x0}
yy=`echo " ( ${y0} + ${Ly} ) - ${dY} * ( ${LoopCount} ) " | bc`
echo ${nCount}" "${xx}" "${yy} >> ${FileBottom}
done
echo "# " >> ${FileBottom}
nEdge=`expr ${nNodes} + 1`
echo "#-------------------------------">> ${FileBottom}
echo ${nNodes}" 0" >> ${FileBottom}
echo "#-------------------------------">> ${FileBottom}
LoopCount=0
Nm1=`expr ${nNodes} - 2`
while [ $LoopCount -le ${Nm1} ] ; do
#while [ $LoopCount -le ${nNodes} ] ; do
LoopCount=`expr $LoopCount + 1`
LC2=`expr $LoopCount + 1`
echo ${LoopCount}" "${LoopCount}" "${LC2} >> ${FileBottom}
done
LoopCount=`expr $LoopCount + 1`
echo ${LoopCount}" "${LoopCount}" 1" >> ${FileBottom}
echo "# " >> ${FileBottom}
echo "0 " >> ${FileBottom}
dL=`echo " 0.5 * ( ${dX} + ${dY} ) " | bc`
dS=`echo ${dL} "*" ${dL} "* 0.25 * sqrt(3)"| bc`
#triangle -pqY ${FileBottom}
triangle -pqa${dS}Y ${FileBottom}
##---------------------------------
## Shewchuk2STL.f
##---------------------------------
FileCtrl="./Shewchuk2STL.ctl"
echo "############ Shewchuk2STL.ctl" > ${FileCtrl}
echo ${FileBottom%.poly}.1.node >> ${FileCtrl}
echo ${FileBottom%.poly}.1.ele >> ${FileCtrl}
echo ${FileBottom%.poly}.stl >> ${FileCtrl}
echo "" >> ${FileCtrl}
./Shewchuk2STL
Y オプションの制御より，シェルスクリプトで，
点列を順序良く出力するループ処理がめんどくさかった．
----------------------------
----------------------------
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