def draw_2d_arrow_s(draw, r, start_pt=np.array([0,0]),
end_pt=np.array([7,-3]), \
origin=np.array([4,10]),scale=64, rgba="grey",
width=3):
pt1 = np.dot(r,start_pt)*scale + origin*scale
pt2 = np.dot(r,end_pt)*scale + origin*scale
draw.line((pt1[0],pt1[1],pt2[0],pt2[1]), fill=rgba, width=width)
vec = (pt2-pt1)
vec = vec/np.sqrt(sum(vec**2))/2
r1 = planar_rotation(5*np.pi/4)
arrow_foot = np.dot(r1,vec)*scale + pt2
draw.line((arrow_foot[0],arrow_foot[1],pt2[0],pt2[1]), fill=rgba, width=width)
r1 = planar_rotation(3*np.pi/4)
arrow_foot = np.dot(r1,vec)*scale + pt2
draw.line((arrow_foot[0],arrow_foot[1],pt2[0],pt2[1]), fill=rgba, width=width)
def tst(basedir=".\\"):
for i in range(11):
im = Image.new("RGB", (512, 512), (0, 0, 0))
draw = ImageDraw.Draw(im, 'RGBA')
end1 = np.array([6.0, 6.0])
end2 = np.array([4.0, 8.0])
end = end1 * (1 - i / 10.0) + end2 * (i / 10.0)
gg=grd.Grid(end=end,\
center=np.array([0,0]),origin=np.array([40,256]),
rot=planar_rotation(-np.pi/4),scale=32)
pt2 = gg.get_grid_pt(end[0], end[1])
gg.draw(draw, width=3)
## Draw horizontal line corresponding to the main diagonal.
pt1 = gg.get_grid_pt(0, 0)
pt2 = gg.get_grid_pt(6, 6)
draw.ellipse((pt2[0]-5, pt2[1]-5, pt2[0]+5, \
pt2[1]+5),fill='red')
draw.line((0, pt2[1], 512, pt2[1]), fill="orange", width=3)
draw.line((0, pt1[1], 512, pt1[1]), fill="purple", width=3)
draw.ellipse((pt1[0]-5, pt1[1]-5, pt1[0]+5, \
pt1[1]+5),fill='blue')
## Draw horizontal line corresponding to one above the main diagonal.
pt1 = gg.get_grid_pt(0, 1)
pt2 = gg.get_grid_pt(5, 6)
#draw.line((pt1[0],pt1[1],pt2[0],pt2[1]), fill="orange", width=2)
im.save(basedir + "im" + str(i) + ".png")
def proof_eqn_line(idx, r=planar_rotation(np.pi * 3 / 20.0)):
mc = MapCoord(im_size=np.array([512, 512]), origin=np.array([4, 4]))
cnv = Canvas(mc)
cnv.draw_grid()
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]))
cnv.draw_2d_arrow(np.array([0, 4]), np.array([0, -4]))
cnv.draw_point(np.array([0, 0]), fill="yellow", size=5)
cnv.write_txt(np.array([0, 0]), "O", (255, 255, 0, 200))
pt1 = np.array([-1, 4])
pt2 = np.array([3, -2])
l = Line(pt1, pt2)
cnv.draw_line(pt1, pt2, fill="purple")
cnv.draw_line(np.array([0, 0]),
l.closest_pt_from_origin * 5,
fill="white",
width=1)
cnv.draw_point(l.closest_pt_from_origin, fill="blue", size=4)
cnv.draw_arrow(np.array([0,0]), l.closest_pt_from_origin*.6,\
fill="blue",width=3,arr_bk=.9,arr_per=.1)
cnv.write_txt(l.closest_pt_from_origin + np.array([.1, .1]), "A", "blue")
arb_pt_1 = pt1 * .2 + pt2 * .8
arb_pt_2 = pt1 * .9 + pt2 * .1
cnv.draw_point(arb_pt_1, fill=(3, 252, 53), size=4)
cnv.draw_point(arb_pt_2, fill=(252, 144, 3), size=4)
cnv.draw_arrow(np.array([0,0]), arb_pt_1,\
fill=(3, 252, 53),width=1,arr_bk=.9,arr_per=.1)
cnv.draw_arrow(np.array([0,0]), arb_pt_2,\
fill=(252, 144, 3),width=1,arr_bk=.9,arr_per=.1)
cnv.write_txt(arb_pt_1 + np.array([.1, .1]), "B", (3, 252, 53))
cnv.write_txt(arb_pt_2 + np.array([.1, .1]), "C", (252, 144, 3))
basedir = '.\\images\\RotatingCube\\'
cnv.im.save(basedir + "im" + str(idx) + ".png")
def eqn_of_line(idx=0, r=planar_rotation(np.pi * 3 / 20.0)):
mc = MapCoord(im_size=np.array([512, 512]), origin=np.array([4, 4]))
cnv = Canvas(mc)
cnv.draw_grid()
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]))
cnv.draw_2d_arrow(np.array([0, 4]), np.array([0, -4]))
cnv.draw_2d_arrow(np.array([0, 0]), np.array([0, -2]), rgba="orange", r=r)
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]), rgba="grey", r=r)
basedir = '.\\images\\RotatingCube\\'
cnv.im.save(basedir + "im" + str(idx) + ".png")
def scaling_w(idx=0, r=planar_rotation(np.pi*3/20.0)):
mc = MapCoord(im_size=np.array([512,512]),origin=np.array([4,4]))
cnv = Canvas(mc)
cnv.draw_grid()
cnv.draw_2d_arrow(np.array([-4,0]), np.array([4,0]))
cnv.draw_2d_arrow(np.array([0,4]), np.array([0,-4]))
eps = zigzag2(idx,0,5,-5)/5
cnv.draw_2d_arrow(np.array([0,0]), np.array([0,-2*(1+eps)]),rgba="orange",r=r)
cnv.draw_2d_arrow(np.array([-4,0]), np.array([4,0]),rgba="white",r=r)
basedir = '.\\images\\RotatingCube\\'
cnv.im.save(basedir + "im" + str(idx) + ".png")
def __init__(self,pt1,pt2):
"""
"""
self.pt1 = pt1
self.pt2 = pt2
self.vec_along = (pt2-pt1)
r = planar_rotation(np.pi/2)
self.w = np.dot(r,self.vec_along)
mod_w_sq = np.dot(self.w,self.w)
self.w = self.w/np.sqrt(mod_w_sq)
# Eqn of line is assumed to be w^T x+b=0
self.b = -np.dot(self.w,self.pt1)
self.closest_pt_from_origin = -self.b*self.w
def basic_grid():
im = Image.new("RGB", (512, 512), (0, 0, 0))
draw = ImageDraw.Draw(im, 'RGBA')
gg=grd.Grid(end=np.array([6.0,6.0]),\
center=np.array([0,0]),origin=np.array([40,256]),
rot=planar_rotation(-np.pi/4),scale=32)
gg.draw(draw, width=3)
## Draw horizontal line corresponding to the main diagonal.
pt1 = gg.get_grid_pt(0, 0)
pt2 = gg.get_grid_pt(6, 6)
draw.line((pt1[0], pt1[1], pt2[0], pt2[1]), fill="purple", width=3)
draw.ellipse((pt1[0]-5, pt1[1]-5, pt1[0]+5, \
pt1[1]+5),fill='blue')
draw.ellipse((pt2[0]-5, pt2[1]-5, pt2[0]+5, \
pt2[1]+5),fill='red')
## Draw horizontal line corresponding to one above the main diagonal.
pt1 = gg.get_grid_pt(0, 1)
pt2 = gg.get_grid_pt(5, 6)
draw.line((pt1[0], pt1[1], pt2[0], pt2[1]), fill="orange", width=2)
return im, draw, gg
## Draw horizontal line corresponding to one above the main diagonal.
pt1 = gg.get_grid_pt(0, 1)
pt2 = gg.get_grid_pt(5, 6)
#draw.line((pt1[0],pt1[1],pt2[0],pt2[1]), fill="orange", width=2)
im.save(basedir + "im" + str(i) + ".png")
#######
for i in range(13):
im = Image.new("RGB", (512, 512), (0, 0, 0))
draw = ImageDraw.Draw(im, 'RGBA')
end2 = np.array([4.0, 8.0])
gg=grd.Grid(end=end2,\
center=np.array([2,-4]),origin=np.array([90,280]),
rot=planar_rotation(-np.pi/4-np.pi*(i/12.0)),scale=32)
gg.draw(draw, width=3)
pt2 = gg.get_grid_pt(end2[0], end2[1])
draw.ellipse((pt2[0]-5, pt2[1]-5, pt2[0]+5, \
pt2[1]+5),fill='red')
draw.line((0, pt2[1], 512, pt2[1]), fill="orange", width=3)
## Draw horizontal line corresponding to the main diagonal.
pt1 = gg.get_grid_pt(0, 0)
pt2 = gg.get_grid_pt(6, 6)
draw.line((0, pt1[1], 512, pt1[1]), fill="purple", width=3)
draw.ellipse((pt1[0]-5, pt1[1]-5, pt1[0]+5, \
pt1[1]+5),fill='blue')
## Draw horizontal line corresponding to one above the main diagonal.
pt1 = gg.get_grid_pt(0, 1)
pt2 = gg.get_grid_pt(5, 6)
import pyray.grid as grd
#from importlib import reload
###
basedir = '.\\Images\\RotatingCube\\'
gg0=grd.Grid(end=np.array([12.0,12.0]),origin=np.array([256,256]),\
center=np.array([3,3]),scale=64/np.sqrt(2))
pt = gg0.get_grid_pt(6, 0)
for i in range(11):
im = Image.new("RGB", (1024, 1024), (0, 0, 0))
draw = ImageDraw.Draw(im, 'RGBA')
gg=grd.Grid(end=np.array([6.0,6.0]),origin=pt,\
center=np.array([0,0]),
rot=planar_rotation(-np.pi*10/10/4))
gg0.draw(draw, fill=(252, 0, 0, 90), width=1)
gg.draw(draw)
im.save(basedir + "im" + str(i) + ".png")
###
basedir = '.\\Images\\RotatingCube\\'
gg=grd.Grid(end=np.array([6.0,6.0]),\
center=np.array([0,0]),origin=np.array([40,430]))
pts = [
gg.get_grid_pt(i, j) for i, j in [(0, 0), (0, 2), (3, 2), (3, 6), (6, 6)]
]
pt1 = gg.get_grid_pt(0, 0)
pt2 = gg.get_grid_pt(6, 6)
import pyray.grid as grd
for i in range(11):
im=Image.new("RGB", (512, 512), (0,0,0))
draw = ImageDraw.Draw(im,'RGBA')
end1=np.array([6.0,6.0])
end2=np.array([4.0,8.0])
end=end1*(1-i/10.0)+end2*(i/10.0)
pt2=gg.get_grid_pt(end[0],end[1])
draw.ellipse((pt2[0]-5, pt2[1]-5, pt2[0]+5, \
pt2[1]+5),fill='red')
draw.line((0,pt2[1],512,pt2[1]), fill="orange", width=3)
gg=grd.Grid(end=end,\
center=np.array([0,0]),origin=np.array([40,256]),
rot=planar_rotation(-np.pi/4),scale=32)
gg.draw(draw,width=3)
## Draw horizontal line corresponding to the main diagonal.
pt1=gg.get_grid_pt(0,0)
pt2=gg.get_grid_pt(6,6)
draw.line((0,pt1[1],512,pt1[1]), fill="purple", width=3)
draw.ellipse((pt1[0]-5, pt1[1]-5, pt1[0]+5, \
pt1[1]+5),fill='blue')
## Draw horizontal line corresponding to one above the main diagonal.
pt1=gg.get_grid_pt(0,1)
pt2=gg.get_grid_pt(5,6)
#draw.line((pt1[0],pt1[1],pt2[0],pt2[1]), fill="orange", width=2)
im.save(basedir + "im" + str(i) + ".png")
def eqn_of_line(idx=0, r=planar_rotation(np.pi * 3 / 20.0)):
mc = MapCoord(im_size=np.array([512, 512]), origin=np.array([4, 4]))
cnv = Canvas(mc)
cnv.draw_grid()
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]))
cnv.draw_2d_arrow(np.array([0, 4]), np.array([0, -4]))
cnv.draw_2d_arrow(np.array([0, 0]), np.array([0, -2]), rgba="orange", r=r)
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]), rgba="grey", r=r)
basedir = '.\\images\\RotatingCube\\'
cnv.im.save(basedir + "im" + str(idx) + ".png")
for i in range(10):
eqn_of_line(i, r=planar_rotation(2 * np.pi * i / 10.0))
def scaling_w(idx=0, r=planar_rotation(np.pi * 3 / 20.0)):
mc = MapCoord(im_size=np.array([512, 512]), origin=np.array([4, 4]))
cnv = Canvas(mc)
cnv.draw_grid()
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]))
cnv.draw_2d_arrow(np.array([0, 4]), np.array([0, -4]))
eps = zigzag2(idx, 0, 5, -5) / 5
cnv.draw_2d_arrow(np.array([0, 0]),
np.array([0, -2 * (1 + eps)]),
rgba="orange",
r=r)
cnv.draw_2d_arrow(np.array([-4, 0]), np.array([4, 0]), rgba="white", r=r)
basedir = '.\\images\\RotatingCube\\'