incentre7.py

#incentre7.py works ok. Puts in 3 yellow bisector lines that meet at incentre
import math
import matplotlib.pyplot as plt
def line_equation2(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    m = (y2 - y1) / (x2 - x1) if x2 != x1 else float('inf')
    b = y1 - m * x1 if m != float('inf') else None
    #print("m,b",m,b)
    return (m,b)
def intersection2(L1,L2): #where L1 is line (m,c)
    m1,b1 = L1
    m2,b2 = L2      #Pb lines here
    if m1 == m2:
        return None  # Lines are parallel
    if m1 == float('inf'):
        x = b1
        y = m2 * x + b2
    elif m2 == float('inf'):
        x = b2
        y = m1 * x + b1
    else:
        x = (b2 - b1) / (m1 - m2)
        y = m1 * x + b1
    return (x, y)       #so returns a point as an ordered pair
def line_equation(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    m = (y2 - y1) / (x2 - x1) if x2 != x1 else float('inf')
    b = y1 - m * x1 if m != float('inf') else None
    return (m, b)
def equations_of_sides_of_triangle(VA,VB,VC):
    Line_AB= line_equation(VA,VB)
    Line_BC= line_equation(VB,VC)
    Line_CA= line_equation(VC,VA)
    return Line_AB,Line_BC,Line_CA
def incentre_info(V1,V2,V3):
##    def line_equation(p1, p2):
##        x1, y1 = p1
##        x2, y2 = p2
##        m = (y2 - y1) / (x2 - x1) if x2 != x1 else float('inf')
##        b = y1 - m * x1 if m != float('inf') else None
    Line_AB= line_equation(V1,V2)
    Line_BC= line_equation(V2,V3)
    Line_CA= line_equation(V3,V1)
    x1,y1=V1
    x2,y2 = V2
    x3,y3 = V3
    # Calculate the lengths of the three sides
    print('Vertices are A,B,C ', x1,y1,x2,y2,x3,y3)

    c = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
    a = math.sqrt((x3 - x2)**2 + (y3 - y2)**2)
    b = math.sqrt((x1 - x3)**2 + (y1 - y3)**2)

    # Calculate the semi-perimeter
    s = (a + b + c) / 2

    # Calculate the area of the triangle
    area = 0.5 * (a * b * math.sin(math.acos((a**2 + b**2 - c**2) / (2 * a * b))))

    # Calculate the center and radius of the incircle
    x_center = (a * x1 + b * x2 + c * x3) / (a + b + c)
    y_center = (a * y1 + b * y2 + c * y3) / (a + b + c)
    I = (x_center,y_center)     #I = incentre
    radius = area / s

    #medianA = line_equation(vertexA,mpBC) #median from A
    angle_bisector_lineA = line_equation2(V1,I) #median from A
    angle_bisector_lineB = line_equation2(V2,I) #median from A
    angle_bisector_lineC = line_equation2(V3,I) #median from A

    foot_of_bisector_of_A = intersection2(angle_bisector_lineA,Line_BC)
    foot_of_bisector_of_B = intersection2(angle_bisector_lineB,Line_CA)
    foot_of_bisector_of_C = intersection2(angle_bisector_lineC,Line_AB)

    angle_bisectors = (angle_bisector_lineA,angle_bisector_lineB,angle_bisector_lineC)
    #angle_bisectors2 = [angle_bisector_lineA,angle_bisector_lineB,angle_bisector_lineC]
    feet_of_angle_bisectors =(foot_of_bisector_of_A, foot_of_bisector_of_B,foot_of_bisector_of_C)
    #return angle_bisector_lineA,angle_bisector_lineB,angle_bisector_lineC, foot_of_bisector_of_A, foot_of_bisector_of_B,foot_of_bisector_of_C
    group_angle_bisectors = I, angle_bisectors, feet_of_angle_bisectors
#    return I, angle_bisectors, feet_of_angle_bisectors #so returns I-tuple, 3 tuples for lines, 3 tuples for feet
    return group_angle_bisectors

vertexA = (0,0)
vertexB =(60,10)
vertexC =(30,60)
angleBisectorInfo = incentre_info(vertexA,vertexB,vertexC)
incentrePoint, bisectors, bisector_feet = angleBisectorInfo
incentrex, incentrey = incentrePoint
fA,fB,fC = bisector_feet
fAx,fAy =fA
fBx,fBy =fB
fCx,fCy =fC

fig, ax = plt.subplots(figsize=(6, 6))
Ax,Ay = vertexA
Bx,By = vertexB
Cx,Cy = vertexC
circle = plt.Circle((incentrex, incentrey), 0.5, fill=False, color='y')
ax.add_artist(circle)
ax.plot([Ax,Bx,Cx,Ax], [Ay,By,Cy,Ay], 'b-', linewidth=2) #this plots the triangle

ax.plot([Ax,fAx], [Ay, fAy], 'y-', linewidth=1)
ax.plot([Bx,fBx], [By, fBy], 'y-', linewidth=1)
ax.plot([Cx,fCx], [Cy, fCy], 'y-', linewidth=1)

plt.show()
three_lines=equations_of_sides_of_triangle(vertexA,vertexB,vertexC)
print("three lines are ", three_lines)

#result = drop_perpendicular(x1,y1, x2, y2, x3, y3):
result=incentre_info(vertexA,vertexB,vertexC)
print(f"incentre information:incentre,angle_bisectors,feet=,{result}")
#print('Area = ', area)
#Find feet of angle_bisectors and sides of triangle ie. where does ..
#..angle_bisector_lineA cut line_BC.
#Use intersection2(L1,L2). ie intersection2(angle_bisector_lineA,line_BC)...
#Call this foot_of_bisector_ofA
#foot_of_bisector_of_A = intersection2(angle_bisector_lineA,line_BC)
#print("Footof bisector of A is ", foot_of_besector_of_A)
#The feet look OK for bisector of A,B but not for C
# No, seems Ok now correction been made.
#Next add incentre coords to final major return statement around line 75
#works ok. See return statement around line 79.