Visuel
Flexible library of graphical algorithms in Python, providing mathematical classes such as vectors and points, speed-optimized graphical functions and much more ! It can be used on the Numworks calculator, or on a computer.
- Short presentation :
- Documentation :
The link to the github project: Visuel
from kandinsky import set_pixel,get_pixel,fill_rect,draw_string,color from math import pi,cos,sin,radians,factorial a,b,perm,distance,milieu,average=lambda P1,P2:(P2.y-P1.y)/(P2.x-P1.x),lambda a,P1:-(a*P1.x-P1.y),lambda n,k:factorial(n)/factorial(n-k),lambda P1,P2:((P2.x-P1.x)**2+(P2.y-P1.y)**2)**0.5,lambda P1,P2,p=2:Point((P1.x+P2.x)/p,(P1.y+P2.y)/p),lambda liste:sum(liste)/len(liste) DrawWithStyle={'O':"fill_circle(P,3,color)",'+':"draw_croix(P,3,0,color)",'*':"draw_croix(P,4,45,color)",'.':"set_pixel(P.x,P.y,color)"} class Point: def __init__(self,x,y,name=''):self.x,self.y,self.name=x,y,name def __str__(self):return str(self.name) def __iter__(self):return iter([self.x,self.y]) def __repr__(self):return "Point({}, {})".format(self.x,self.y) def __eq__(self,other):return (self.x==other.x)and(self.y==other.y) if isinstance(other,Point) else False def round(self):self.x,self.y=round(self.x),round(self.y) def copy(self):return Point(self.x,self.y,self.name) class Vector: def __init__(self,P1=None,P2=None,x=None,y=None,name=''):cond=(P1!=None and P2!=None);self.x,self.y,self.name=P2.x-P1.x if cond else x,P2.y-P1.y if cond else y,name def __str__(self):return str(self.name) def __iter__(self):return iter([self.x,self.y]) def __repr__(self):return "Vector({}, {})".format(self.x,self.y) def __eq__(self,other):return (self.x==other.x)and(self.y==other.y) if isinstance(other,Vector) else False def __add__(self,other):return Vector(x=self.x+other.x,y=self.y+other.y) if isinstance(other,Vector) else Point(other.x+self.x,other.y+self.y) if isinstance(other,Point) else None def __sub__(self,other):return Vector(x=self.x-other.x,y=self.y-other.y) if isinstance(other,Vector) else Point(other.x-self.x,other.y-self.y) if isinstance(other,Point) else None def __mul__(self,other):return Vector(x=self.x*other.x,y=self.y*other.y) if isinstance(other,Vector) else Vector(x=self.x*other,y=self.y*other) if isinstance(other,(int,float)) else None def __truediv__(self,other):return Vector(x=self.x/other.x,y=self.y/other.y) if isinstance(other,Vector) else Vector(x=self.x/other,y=self.y/other) if isinstance(other,(int,float)) else None def rotate(self,angle):angle=radians(angle);return Vector(x=self.x*cos(angle)-self.y*sin(angle),y=self.x*sin(angle)+self.y*cos(angle),name=self.name) def neg(self):return Vector(x=-self.x,y=-self.y,name=self.name) def copy(self):return Vector(x=self.x,y=self.y,name=self.name) def round(self):self.x=round(self.x);self.y=round(self.y) def expend(liste,d,M=None):M=Point(round(average([P.x for P in liste])),round(average([P.y for P in liste]))) if M==None else M;return [Point(round(P.x+(P.x-M.x)*d),round(P.y+(P.y-M.y)*d)) if d!=0 else P for P in liste] def connect_points(liste,ending=False):line=[(liste[p],liste[p+1]) for p in range(len(liste)) if p<len(liste)-1];line.append((liste[-1],liste[0])) if ending else None;return line def findWithPoint(P1,P2,length):N=distance(P1,P2);return Point(P1.x+((P2.x-P1.x)*length)/N,P1.y+((P2.y-P1.y)*length)/N) def alpha_pixel(x,y,col,alpha=1.0):set_pixel(x,y,tuple(C1*alpha-C2*alpha+C2 for C1,C2 in zip(color(col),get_pixel(x,y)))) def interpolate(C1,C2,N=100):C1,C2=color(C1),color(C2);interpolated_colors=[(C1[0]+(C2[0]-C1[0])*i/(N+1),C1[1]+(C2[1]-C1[1])*i/(N+1),C1[2]+(C2[2]-C1[2])*i/(N+1)) for i in range(N+2)];return interpolated_colors[1:-1] def scatter(X,Y,color='0',style='*',C=Point(160,111)):draw_points([Point(round(C.x+x),round(C.y-y)) for x,y in zip(X,Y)],color,style,False) def plot(X,Y,color='0',C=Point(160,111)):set_lines(connect_points([Point(round(C.x+x),round(C.y-y)) for x,y in zip(X,Y)]),color) def draw_points(liste,color='0',style="*",text=True): for P in liste:exec(DrawWithStyle[style],{'P':P,"color":color,"set_pixel":set_pixel,"fill_circle":fill_circle,"draw_croix":draw_croix});draw_string(str(P.name),P.x+6,P.y+6,'0','1')if text else None def draw_croix(center,r,angle=90,color='0'): R=Vector(center,Point(center.x+r,center.y));R=R.rotate(angle) for _ in range(4):R=R.rotate(90);R.round();set_lines([(center,R+center)],color) def set_lines(line,color='0'): for P1,P2 in line: up,right=True if P2.y>P1.y else False,True if P2.x>P1.x else False;h,b=P2.y-P1.y if up else P1.y-P2.y,P2.x-P1.x if right else P1.x-P2.x;n=True if h<=b else False;set_pixel(P2.x,P2.y,color) if b!=0 or h!=0:e=h/b if n else b/h for i in range(b if n else h):set_pixel(int(round(P1.x+i) if right else round(P1.x-i))if n else int(round(P1.x+e*i) if right else round(P1.x-e*i)),int(round(P1.y+e*i) if up else round(P1.y-e*i))if n else int(round(P1.y+i) if up else round(P1.y-i)),color) def draw_arrows(liste,color='0',length=10,angle=45,fill=False): for A,B in liste:V1=Vector(findWithPoint(B,A,length),B).neg();V2,V3=V1.rotate(angle),V1.rotate(-angle);V2.round();V3.round();set_lines([(A,B)],color);set_lines([(B,V2+B),(B,V3+B)],color) if not fill else fill_triangles([(V2+B,B,V3+B)],color) def draw_vector(P,V,color='0'):x,y=milieu(P,V+P);draw_arrows([(P,V+P)],color,fill=False);draw_string(str(V.name),round(x-6),round(y-6),'0','1') def draw_droite(P1,P2,color='0',name=None): if P1.x==P2.x:set_lines([(Point(P1.x,0),Point(P1.x,222))],color) elif P1.y==P2.y:set_lines([(Point(0,P1.y),Point(320,P1.y))],color) else: _a=a(P1,P2);_b=b(_a,P2);P0,P3=Point(round((222-_b)/_a),222) if abs(P2.x-P1.x)<abs(P2.y-P1.y) else Point(0,round(_a*0+_b)),Point(round((-1-_b)/_a),-1) if abs(P2.x-P1.x)<abs(P2.y-P1.y) else Point(320,round(_a*320+_b));set_lines([(P0,P3)],color) if name!=None:M=milieu(P1,P2);draw_string(str(name),round(M.x-6),round(M.y-6),'0','1') def fill_triangles(liste,color='0',alpha=1): eq=lambda p,a,b:(a.x-p.x)*(b.y-p.y)-(a.y-p.y)*(b.x-p.x) for P1,P2,P3 in liste: xmin,xmax,ymin,ymax=min(P1.x,P2.x,P3.x),max(P1.x,P2.x,P3.x)+1,min(P1.y,P2.y,P3.y),max(P1.y,P2.y,P3.y)+1;width,height=abs(xmax+xmin),abs(ymax+ymin) for y in range(ymin,ymax): if 0<=y<height: for x in range(xmin,xmax): pos=Point(x,y);w1,w2,w3=eq(pos,P3,P1),eq(pos,P1,P2),eq(pos,P2,P3) if 0<=x<width and ((w1>=0 and w2>=0 and w3>=0) or (-w1>=0 and -w2>=0 and -w3>=0)):set_pixel(x,y,color) if alpha==1 else alpha_pixel(x,y,color,alpha) def draw_polygone(n,rayon,coord,color='0'):alpha=2*pi/n;set_lines(connect_points([Point(round(coord.x+rayon*cos(k*alpha)),round(coord.y+rayon*sin(k*alpha)),color) for k in range(1,n+1)],True),color) def fill_polygone(n,rayon,coord,color='0',c_map=None,alpha=1): _alpha=2*pi/n;points=[Point(round(coord.x+rayon*cos(k*_alpha)),round(coord.y+rayon*sin(k*_alpha))) for k in range(1,n+1)] for p,c in zip(connect_points(points,True),[color for _ in range(len(points))] if not isinstance(c_map,list) else c_map):fill_triangles([([coord,p[0],p[1]])],c,alpha) def draw_rectangle(P1,P4,color='0'):fill_rect(P1.x,P1.y,P4.x-P1.x,1,color);fill_rect(P4.x,P1.y,1,P4.y-P1.y+1,color);fill_rect(P1.x,P4.y,P4.x-P1.x,1,color);fill_rect(P1.x,P1.y,1,P4.y-P1.y,color) def fill_rectangle(P1,P4,color='0',alpha=1): for x,y in [(x,y) for x in range(P4.x-P1.x if P4.x>P1.x else P1.x-P4.x) for y in range(P4.y-P1.y if P4.y>P1.y else P1.y-P4.y)]:alpha_pixel(P1.x+x,P1.y+y,color,alpha) def draw_circle(center,rayon,color='0'): for x in range(-abs(rayon),abs(rayon)): l=round((abs(rayon)**2-x**2)**0.5) if abs(x)<=l:set_pixel(center.x+l,center.y+x,color);set_pixel(center.x-l,center.y-x,color);set_pixel(center.x-x,center.y-l,color);set_pixel(center.x+x,center.y+l,color) def fill_circle(center,rayon,color='0',alpha=1): for x,y in [(x,y) for x in range(-round(rayon),round(rayon)+1) for y in range(-round(rayon),round(rayon)+1)]: if round(distance(center,Point(center.x+x,center.y+y)))<=rayon:alpha_pixel(center.x+x,center.y+y,color,alpha) if alpha!=1 else set_pixel(center.x+x,center.y+y,color) def bezier_curve(liste,color='0',thickness=1,N=1500): for _t in range(N): x,y,t=0,0,_t/N for i in range(len(liste)):x+=((perm(len(liste)-1,i)/factorial(i))*(t**i)*((1-t)**(len(liste)-1-i)))*liste[i].x;y+=((perm(len(liste)-1,i)/factorial(i))*(t**i)*((1-t)**(len(liste)-1-i)))*liste[i].y P=Point(round(x),round(y));set_pixel(P.x,P.y,color) if thickness==1 else fill_circle(P,thickness,color,1)