Leave record about python coding
CUDAはNVIDIAが開発・提供しているGPU向けの汎用並列コンピューティングプラットフォーム。専用のC/C++コンパイラ (nvcc) やライブラリ (API) などが提供されている(wiki)。
NVIDIAのサイトからOS/アーキテクチャにあったToolkitをダウンロード。
https://developer.nvidia.com/cuda-downloads
※wget方式でのコマンドラインが指定される。
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wget https://developer.download.nvidia.com/compute/cuda/11.5.1/local_installers/cuda_11.5.1_495.29.05_linux.run sudo sh cuda_11.5.1_495.29.05_linux.run |
acceptと入力してEnter
とりあえず全部にチェック入れてInstall
インストールの際はUIをGUIからCUIに変更しておく(参考)。
インストールした結果が下記
centos7にてGeForce GTX 1060を使えるようにする為、
NVIDIAのドライバインストールをする。
現在利用可能なVGAの確認
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% lspci | grep VGA |
cpuに搭載されているUHD Graphics 630とGeForce GTX 1060 6GBが認識されていることが確認できる。
NVIDIAのサイトから上記に対応したドライバをダウンロード
https://www.nvidia.co.jp/Download/index.aspx?lang=jp
システム起動時のUIをGUIからCUIに変更しておく
default.targetのリンク先をGUI時のgraphical.targetから
CUI用のmulti-user.targetに変更する。
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% cd /etc/systemd/system % sudo unlink default.target % sudo ln -s multi-user.target default.target |
システムに反映させて再起動させる
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% sudo dracut --force % sudo reboot |
ダウンロードしたドライバをインストールする
bash NVIDIA-Linux-x86_64-470.94.run
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bash NVIDIA-Linux-x86_64-470.94.run |
インストールが完了したら下記コマンドでグラフィックカードの状態を確認することができる。
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% nvidia-smi |
OSはubunts 18
%pip3 install PyOpenGL PyOpenGL_accelerate
python3でmatplotlibのインストールメモ
OSはUbuntu 18.04.5 LTS
コマンドは下記
%pip3 install matplotlib
python3でopenCVのインストールメモ
OSはUbuntu 18.04.5 LTS
コマンドは下記
%sudo apt install python3-opencv
ある点(x,y)が多角形の内部にあるかどうかを判定するアルゴリズム
An algorithm to determine if a point (x, y) is inside a polygon
ある点(x,y)が多角形の内部にあるかどうかを判定する
判定のアルゴリズムは以下３ステップ
・判定対象としたい多角形の、最も大きいx座標を求める(xp)。
・判定対象とした点から、x軸並行で上記で求めたxpまでの線分を作成する(lxp)
・線分lxpと多角形を構成するエッジとの交点の数をカウントする(cross num)。
→交点の数が・・
奇数なら、点(x,y)は多角形の内部にある。
偶数なら、点(x,y)は多角形の外部にある。
It is judged whether or not a certain point (x, y) is inside the polygon
The algorithm of the judgment consists of three steps
· Find the largest x coordinate of the polygon you want to judge (xp).
· Create a line segment up to xp obtained in parallel on the x axis from the point to be judged (lxp)
· Count the number of intersection points between the line segment lxp and the edge constituting the polygon (cross num).
→ Number of intersection points
If it is odd, the point (x, y) is inside the polygon.
If it is an even number, the point (x, y) is outside the polygon.
make center line at polygons , using voronoi.
ポリゴンを構成する頂点列から、ポリゴン内に中心線を生成する。中心線の生成にはボロノイ図を用いる。入力としたポリゴン内の長いエッジに対しては細分化を行い、ボロノイ図を生成。生成したボロノイ図を構成するエッジの内、ポリゴン内にあるもののみを抽出すると、そのエッジはポリゴンの中心線のような形状となる。
generate center line in the polygon from the vertex sequence constituting the polygon. at generate we use voronoi diagrams . For long edges in the input polygon, subdivide it and generate Voronoi diagram. When extracting only those in the polygon out of the edges constituting the generated Voronoi diagram, the edge has a shape like the center line of the polygon.
なお、今回扱うポリゴン頂点列のフォーマットしては下記の様なものとしてある。ポリゴンが複数ある場合は、下記を一つのテキストファイルに複数記述することで複数ポリゴンを表現できる。
The format of the polygon vertex sequence handled this time is as follows. If there are multiple polygons, you can express multiple polygons by describing the following in one text file.
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XY <point num> <x1> <y1> <x2> <y2> <x3> <y3> <x4> <y5> .... .... |
XY .. 固定(fixed)
point num .. ポリゴンを形成する頂点数
(number of vertives forming a polygon)
x1 y1 .. 頂点１つを表すX-Y座標。
(XY coordinates representing one vertex)
■頂点座標指定のイメージ図(format sample image)
最初に生成する中心線の結果画像を示す。青色がポリゴン図形、白線がボロノイ図、緑線が中心線となる。
At first, show results image of the center line generated. Blue is a polygon figure, a white line is a Voronoi diagram, and a green line is a center line.
入力としたポリゴン頂点を表すテキストファイルは下記
the input polygon vertex text is as follow URL.
http://hello-python.com/imgs/201901/point_list
■sample code
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import cv2 import sys import math import numpy as np def isEven(num): if num % 2 == 0: return True else: return False def calc_dist(v): x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 xxyy = xx*xx + yy*yy dist = math.sqrt(xxyy) return dist def split_vect(v,slen): tp = np.empty((0,2), float) dist = calc_dist(v) if dist < slen: x1 = v[0] y1 = v[1] tp = np.append(tp, np.array([[x1,y1]]), axis=0) else: snum = int(math.ceil(dist/slen)) x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 dx = xx/snum dy = yy/snum for i in range(snum): xx = x1 + dx * i yy = y1 + dy * i tp = np.append(tp, np.array([[xx,yy]]), axis=0) return tp def convert2vector(oarr): varr = np.empty((0,4), float) for i in range(len(oarr)): xx1 = oarr[i][0] yy1 = oarr[i][1] if i != len(oarr) -1: xx2 = oarr[i + 1][0] yy2 = oarr[i + 1][1] else: xx2 = oarr[0][0] yy2 = oarr[0][1] i = i + 1 varr = np.append(varr, np.array([[xx1,yy1,xx2,yy2]]), axis=0) return varr def convert2vector_s(oarrs): """ convert point list to vector list """ varrs = [] for oarr in oarrs: varr = convert2vector(oarr) varrs.append(varr) return varrs def split_longedge(oarrs, slen): """ if 2points distance is long than slen, make new point between 2points. return new point list. """ # ----------------------------------- # convert point list to vector list # ----------------------------------- varrs = convert2vector_s(oarrs) # ----------------------------------- # split long vector, and convert vector list to point list # ----------------------------------- arrs = [] for varr in varrs: arr = np.empty((0,2),float) for p in varr: tp = split_vect(p,slen) arr = np.append(arr, tp, axis=0) arrs.append(arr) return arrs def adjust_picture_size(arrs,width): minx = sys.maxsize miny = sys.maxsize maxx = -minx maxy = -miny for arr in arrs: for p in arr: xx = p[0] yy = p[1] if xx > maxx: maxx = xx if yy > maxy: maxy = yy if xx < minx: minx = xx if yy < miny: miny = yy wx = maxx - minx wy = maxy - miny w = width h = int(w * wy/wx) # adjust coordinates according to pixel size for j in range(len(arrs)): for i in range(len(arrs[j])): xxx = arrs[j][i][0] - minx xxx = xxx * (w-20)/wx arrs[j][i][0] = xxx yyy = arrs[j][i][1] - miny yyy = yyy * (h-20)/wy arrs[j][i][1] = yyy retval = (arrs, h) return retval def isCross(p1,p2,p3,p4): t1 = (p1[0] - p2[0]) * (p3[1] - p1[1]) + (p1[1] - p2[1]) * (p1[0] - p3[0]) t2 = (p1[0] - p2[0]) * (p4[1] - p1[1]) + (p1[1] - p2[1]) * (p1[0] - p4[0]) t3 = (p3[0] - p4[0]) * (p1[1] - p3[1]) + (p3[1] - p4[1]) * (p3[0] - p1[0]) t4 = (p3[0] - p4[0]) * (p2[1] - p3[1]) + (p3[1] - p4[1]) * (p3[0] - p2[0]) return t1*t2<0 and t3*t4<0 def select_inpol(faces, arrs): ret_vect = np.empty((0,4), int) for p in faces: xx = p[len(p) - 1][0] yy = p[len(p) - 1][1] p = np.append(p, np.array([[xx,yy]]), axis=0) varr = convert2vector(p) ret_vect = np.vstack((ret_vect, varr)) maxx = maxy = -sys.maxsize for arr in arrs: for p in arr: if p[0] > maxx: maxx = p[0] if p[1] > maxy: maxy = p[1] maxx = maxx + 100 pol_vector_s = convert2vector_s(arrs) v_in_pol = np.empty((0,4), float) for vv in ret_vect: v_st = (vv[0], vv[1]) v_ed = (maxx, vv[1]) cross_cnt = 0 for pol_vector in pol_vector_s: for pv in pol_vector: p_st = (pv[0], pv[1]) p_ed = (pv[2], pv[3]) if isCross(v_st, v_ed, p_st, p_ed): cross_cnt += 1 if isEven(cross_cnt): continue else: v_st = (vv[2], vv[3]) v_ed = (maxx, vv[3]) cross_cnt = 0 for pol_vector in pol_vector_s: for pv in pol_vector: p_st = (pv[0], pv[1]) p_ed = (pv[2], pv[3]) if isCross(v_st, v_ed, p_st, p_ed): cross_cnt += 1 if isEven(cross_cnt): continue else: v_in_pol = np.append(v_in_pol, [vv], axis=0) return v_in_pol if __name__ == '__main__': #Specify the width of Voronoi image in pixel size. Height is #calculated automatically from input data and specified width. width = 500 #------------------- #read input data and stack at ndarray(oarr). #------------------- in_data = open("./point_list") lines = in_data.readlines() oarr = np.empty((0,2), float) oarrs = [] pnum = cnt = 0 for i in range(len(lines)): lines[i].strip() jj = lines[i].split() if jj[0] == "XY": pnum = int(jj[1]) else: xx = float(jj[0]) yy = float(jj[1]) oarr = np.append(oarr, np.array([[xx,yy]]), axis=0) cnt += 1 print (pnum,cnt) if cnt == pnum: oarrs.append(oarr) oarr = np.empty((0,2), float) cnt = 0 i = i + 1 #------------------- #split long edge. output is arr. #------------------- split_length = 0.5 arrs = split_longedge(oarrs, split_length) #------------------- #adjust point list coodinate for picture size. output is pts. #------------------- ret = adjust_picture_size(arrs,width) pts_s = ret[0] hight = ret[1] #------------------- #Draw Filled polygon contour. #------------------- img = np.zeros((hight, width, 3), np.uint8) for pts in pts_s: arr0 = np.empty((0,2), int) for p in pts: xx = int(p[0]) yy = int(p[1]) arr0 = np.append(arr0, np.array([[xx,yy]]), axis=0) cv2.fillPoly(img, [arr0], (255, 60, 60)) cv2.imwrite('001_c_pattern_contour.png', img) #------------------- #Draw polygon point mark #------------------- img_draw = img.copy() for pts in pts_s: for p in pts: nnn = np.array([ int(p[0]), int(p[1]) ]) cv2.drawMarker(img_draw, tuple(nnn), (255, 255, 255),\ thickness=1) cv2.imwrite('002_c_point_marker.png', img_draw) #------------------- #Make subdivision surface. #------------------- rect = (0, 0, width, hight) subdiv = cv2.Subdiv2D(rect) for pts in pts_s: for p in pts: #print(p) subdiv.insert((p[0], p[1])) triangles = subdiv.getTriangleList() pols = triangles.reshape(-1, 3, 2) cv2.polylines(img_draw, pols.astype(int), True, (0, 0, 255),\ thickness=1) cv2.imwrite('003_c_delaunay_traiangle.png', img_draw) #------------------- #Make voronoi picture. #------------------- faces, centers = subdiv.getVoronoiFacetList([]) cv2.polylines(img_draw, [f.astype(int) for f in faces], True,\ (255, 255, 255), thickness=2) cv2.imwrite('004_c_voronoi.png', img_draw) #------------------- #select polygon inner edge from voronoi img #------------------- vlist = select_inpol(faces, arrs) for p in vlist: cv2.line(img_draw, (int(p[0]), int(p[1])), (int(p[2]), int(p[3])),\ (0,255,0),thickness=7) cv2.imwrite('005_c_inpol_vol_pnt.png', img_draw) |
テキスト形式で保存された、polygonを形成する頂点列から、ボロノイ図を作成する。初めに入力とする座標データ、次に生成結果の画像(入力図形のダンプや、結果のボロノイ図)、最後に使用したコードを示す。
Create a Voronoi diagram from a vertex sequence that forms a polygon, saved in text format. The first coordinate data input, the resulting image (input figure dump, result Voronoi diagram), and the last used code are shown.
■input point list(x-y coodinate)
-125.458 131.465
-125.474 135.003
-122.966 135.026
-122.974 132.982
-123.492 132.974
-123.516 134.484
-124.011 134.492
-123.988 133.981
-124.515 133.981
-124.491 133.454
-125.026 133.477
-125.018 131.968
-124.459 131.992
-124.53 132.99
-124.019 132.982
-123.98 132.518
-122.769 132.503
-122.785 135.482
-125.513 135.522
-125.521 135.986
-119.97 135.986
-119.947 133.477
-120.442 133.485
-120.442 131.496
-121.527 131.473
-121.535 133.485
-121 133.485
-121.016 134.468
-120.505 134.468
-120.497 135.506
-121.511 135.506
-121.488 133.981
-122.006 133.981
-121.999 131.512
-125.458 131.465
■output picture
001_pattern_contour.png(input pattern)
002_point_marker.png(after split long edge points)
003_delaunay_traiangle.png
004_voronoi.png
■sample code
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import cv2 import sys import math import numpy as np def calc_dist(v): x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 xxyy = xx*xx + yy*yy dist = math.sqrt(xxyy) return dist def split_vect(v,slen): tp = np.empty((0,2), float) dist = calc_dist(v) if dist < slen: x1 = v[0] y1 = v[1] tp = np.append(tp, np.array([[x1,y1]]), axis=0) else: snum = int(math.ceil(dist/slen)) x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 dx = xx/snum dy = yy/snum for i in range(snum): xx = x1 + dx * i yy = y1 + dy * i tp = np.append(tp, np.array([[xx,yy]]), axis=0) return tp def split_longedge(oarr, slen): """ if 2points distance is long than slen, make new point between 2points. return new point list. """ # ----------------------------------- # convert point list to vector list # ----------------------------------- varr = np.empty((0,4), float) for i in range(len(oarr)): xx1 = oarr[i][0] yy1 = oarr[i][1] if i != len(oarr) -1: xx2 = oarr[i + 1][0] yy2 = oarr[i + 1][1] else: break varr = np.append(varr, np.array([[xx1,yy1,xx2,yy2]]), axis=0) i = i + 1 # ----------------------------------- # split long vector, and convert vector list to point list # ----------------------------------- arr = np.empty((0,2),float) for p in varr: tp = split_vect(p,slen) arr = np.append(arr, tp, axis=0) arr0 = np.array([[arr[0][0], arr[0][1]]]) arr = np.append(arr, arr0, axis=0) return arr def adjust_picture_size(arr,width): minx = sys.maxsize miny = sys.maxsize maxx = -minx maxy = -miny for p in arr: xx = p[0] yy = p[1] if xx > maxx: maxx = xx if yy > maxy: maxy = yy if xx < minx: minx = xx if yy < miny: miny = yy wx = maxx - minx wy = maxy - miny w = width h = int(w * wy/wx) # adjust coordinates according to pixel size for i in range(len(arr)): xxx = arr[i][0] - minx xxx = xxx * (w-20)/wx arr[i][0] = xxx yyy = arr[i][1] - miny yyy = yyy * (h-20)/wy arr[i][1] = yyy retval = (arr, h) return retval if __name__ == '__main__': #Specify the width of Voronoi image in pixel size. Height is #calculated automatically from input data and specified width. width = 500 #------------------- #read input data and stack at ndarray(oarr). #------------------- in_data = open("./pol_list") lines = in_data.readlines() oarr = np.empty((0,2), float) for i in range(len(lines)): lines[i].strip() jj = lines[i].split() xx = float(jj[0]) yy = float(jj[1]) oarr = np.append(oarr, np.array([[xx,yy]]), axis=0) i = i + 1 #------------------- #split long edge. output is arr. #------------------- split_length = 0.5 arr = np.empty((0,2),float) arr = split_longedge(oarr, split_length) #------------------- #adjust point list coodinate for picture size. output is pts. #------------------- ret = adjust_picture_size(arr,width) pts = ret[0] hight = ret[1] #------------------- #Draw Filled polygon contour. #------------------- img = np.zeros((hight, width, 3), np.uint8) arr0 = np.empty((0,2), int) for p in pts: xx = int(p[0]) yy = int(p[1]) arr0 = np.append(arr0, np.array([[xx,yy]]), axis=0) cv2.fillPoly(img, [arr0], (255, 60, 60)) cv2.imwrite('001_pattern_contour.png', img) #------------------- #Draw polygon point mark #------------------- img_draw = img.copy() for p in pts: nnn = np.array([ int(p[0]), int(p[1]) ]) cv2.drawMarker(img_draw, tuple(nnn), (255, 255, 255),\ thickness=1) cv2.imwrite('002_point_marker.png', img_draw) #------------------- #Make subdivision surface. #------------------- rect = (0, 0, width, hight) subdiv = cv2.Subdiv2D(rect) for p in pts: print(p) subdiv.insert((p[0], p[1])) triangles = subdiv.getTriangleList() pols = triangles.reshape(-1, 3, 2) cv2.polylines(img_draw, pols.astype(int), True, (0, 0, 255),\ thickness=1) cv2.imwrite('003_delaunay_traiangle.png', img_draw) #------------------- #Make voronoi picture. #------------------- faces, centers = subdiv.getVoronoiFacetList([]) cv2.polylines(img_draw, [f.astype(int) for f in faces], True,\ (255, 255, 255), thickness=2) cv2.imwrite('004_voronoi.png', img_draw) |
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arr = split_longedge(oarr, split_length) |
上記の関数では、頂点列で表すPolygon図形を構成するエッジのうち、任意の長さ以上のエッジに対して分割し頂点を増やすことを行う
In the above function, divide the edges of arbitrary length out of the edges constituting the polygon figure represented by the vertex sequence and increase the number of vertices.input first argument is ndarray(xy point list),second is split length. If distance between two points constituting an edge far than this length, add new point at between two point, and split long edge.
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ret = adjust_picture_size(arr,width) pts = ret[0] hight = ret[1] |
上記の関数では、生成するボロノイ図の画像データのに合わせて、頂点列の座標を変換(倍率変換)している。2つ目引数に指定した値が生成画像の横幅となる。戻り値は配列となっており、一つ目は変換結果のndarray,2つ目は画像の高さ。
In the above function, the coordinates of the vertex sequence are converted (magnification conversion) in accordance with the image data of the generated Voronoi diagram. The value specified for the second argument is the width of the generated image.The return value is an array, the first is the ndarray of the conversion result, the second is the height of the image.
頂点列で表すPolygon図形を構成するエッジのうち、任意の長さ以上のエッジに対して分割し頂点を増やす処理。
Process of dividing vertices of arbitrary length and increasing vertex among edges constituting Polygon figure represented by vertex sequence.
(results sample picture)
@red points : Polygon points
@blue pattern : Filled polygon
before
after
(results split edge)
original_points
[[237.894 0. ]
[130.554 105.408]
[ 43.748 0.626]
[ 0. 42.589]
[129.559 189. ]
[280. 42.589]
[237.894 0. ]]
after split points
[[237.894 0. ]
[184.224 52.704 ]
[130.554 105.408 ]
[ 87.151 53.017 ]
[ 43.748 0.626 ]
[ 0. 42.589 ]
[ 64.7795 115.7945 ]
[129.559 189. ]
[179.706 140.19633333]
[229.853 91.39266667]
[280. 42.589 ]
[237.894 0. ]]
sample code
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import cv2 import sys import math import numpy as np def calc_vabs(v): x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 xxyy = xx*xx + yy*yy dist = math.sqrt(xxyy) return dist def split_vect(v,slen): tp = np.empty((0,2), float) dist = calc_vabs(v) if dist < slen: x1 = v[0] y1 = v[1] tp = np.append(tp, np.array([[x1,y1]]), axis=0) else: snum = int(math.ceil(dist/slen)) x1 = v[0] y1 = v[1] x2 = v[2] y2 = v[3] xx = x2 - x1 yy = y2 - y1 dx = xx/snum dy = yy/snum for i in range(snum): xx = x1 + dx * i yy = y1 + dy * i tp = np.append(tp, np.array([[xx,yy]]), axis=0) return tp def split_longedge(oarr, slen): """ if 2points distance is long than slen, make new point between 2points. return new point list. """ # ----------------------------------- # convert point list to vector list # ----------------------------------- varr = np.empty((0,4), float) for i in range(len(lines)): lines[i].strip() jj = lines[i].split() xx1 = float(jj[0]) yy1 = float(jj[1]) if i != len(lines) -1: lines[i+1].strip() jj = lines[i+1].split() xx2 = float(jj[0]) yy2 = float(jj[1]) else: break varr = np.append(varr, np.array([[xx1,yy1,xx2,yy2]]), axis=0) i = i + 1 # ----------------------------------- # split long vector, and convert vector list to point list # ----------------------------------- arr = np.empty((0,2),float) for p in varr: tp = split_vect(p,slen) arr = np.append(arr, tp, axis=0) arr0 = np.array([[arr[0][0], arr[0][1]]]) arr = np.append(arr, arr0, axis=0) return arr def output2picture(arr, pic_name): w = 200 h = 300 img = np.zeros((w, h, 3), np.uint8) arr0 = np.empty((0,2), int) for p in arr: xx = int(p[0]) yy = int(p[1]) arr0 = np.append(arr0, np.array([[xx,yy]]), axis=0) cv2.fillPoly(img, [arr0], (255, 60, 60)) for p in arr: nnn = np.array([int(p[0]), int(p[1])]) cv2.drawMarker(img, tuple(nnn), (0, 0, 255), thickness=2) cv2.imwrite(pic_name, img) if __name__ == '__main__': in_data = open("./polygon_points.txt") lines = in_data.readlines() oarr = np.empty((0,2), float) for i in range(len(lines)): lines[i].strip() jj = lines[i].split() xx = float(jj[0]) yy = float(jj[1]) oarr = np.append(oarr, np.array([[xx,yy]]), axis=0) i = i + 1 arr = np.empty((0,2),float) #------------------------------------------------- # split function.second argument is split length. arr = split_longedge(oarr,100) #------------------------------------------------- print("\noriginal_points\n",oarr) print("\nafter split points\n",arr) output2picture(oarr,"01_original_points.png") output2picture(arr ,"02_split_points.png") |
■polygon_points.txt
237.894 0.000
130.554 105.408
43.748 0.626
0.000 42.589
129.559 189.000
280.000 42.589
237.894 0.000
頂点座標を空のnumpy.ndarrayに追加する操作。
よくやるのでメモ。
—(sample code)—–
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import cv2 import numpy as np ## cat pol_int (x-y point list) ## -126 133 ## -126 131 ## -117 131 ## -117 134 in_data = open("./plist") lines = in_data.readlines() arr = np.empty((0,2), int) for i in range(len(lines)): lines[i].strip() jj = lines[i].split() xx = int(jj[0]) yy = int(jj[1]) arr = np.append(arr, np.array([[xx, yy]]), axis=0) i = i + 1 print(arr) |
—(exec result)—–
[[-126 133]
[-126 131]
[-117 131]
[-117 134]]
—(memo)—-
initialize ndarray for x-y point list.
at first array is empty(no entry) and add_type is [x,y].
so initialize parameter is (0,2).
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arr = np.empty((0,2), int) |
if append for ndarray, append element must ndarray.
we use only 1 axis, so axis = 0(axis memo)
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arr = np.append(arr, np.array([[xx, yy]]), axis=0) |