import turtle
from math import cos, sin, pi, radians

def move_to(x, y):
    t.penup(); t.goto(x, y); t.pendown()

def filled_rect(x1, y1, x2, y2, fill, outline="black"):
    t.pencolor(outline)
    t.fillcolor(fill)
    move_to(x1, y1)
    t.begin_fill()
    t.goto(x2, y1)
    t.goto(x2, y2)
    t.goto(x1, y2)
    t.goto(x1, y1)
    t.end_fill()

def draw_oval(cx, cy, rx, ry, tilt=0, fill=None, steps=180):
    """Parametric ellipse; steps controls smoothness."""
    ang = radians(tilt)
    def R(x, y):  # rotate (x,y) by tilt
        return (x*cos(ang) - y*sin(ang), x*sin(ang) + y*cos(ang))

    t.fillcolor(fill if fill else "")
    move_to(cx + rx, cy)  # start at angle 0
    if fill:
        t.begin_fill()
    for i in range(1, steps + 1):
        theta = 2*pi*i/steps
        x, y = rx*cos(theta), ry*sin(theta)
        xr, yr = R(x, y)
        t.goto(cx + xr, cy + yr)
    if fill:
        t.end_fill()

def poly(points, fill=None):
    if fill: t.fillcolor(fill); t.begin_fill()
    move_to(*points[0])
    for p in points[1:]:
        t.goto(*p)
    t.goto(*points[0])
    if fill: t.end_fill()

def right_triangle(ax, ay, leg1, leg2, angle=0, fill=None):
    """Right angle at (ax, ay). leg1 along 'angle' degrees, leg2 perpendicular."""
    a = radians(angle)
    B = (ax + leg1*cos(a), ay + leg1*sin(a))            # along angle
    C = (ax - leg2*sin(a), ay + leg2*cos(a))            # 90° to the left
    poly([(ax, ay), B, C], fill=fill)