Bezier Curve for McDonald's Logo

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2019-06-06 04:55

This example demonstrates how to draw the McDonald's logo using Bezier curves. It involves core mathematical concepts such as vectors, geometric constructions, and parametric equations. Key GeoGebra commands used include Midpoint, Vector, OrthogonalVector, CurveCartesian, Line, Intersect, LineBisector, Polygon, Mirror, Circle, OrthogonalLine, and Segment. Suitable for high school students and those interested in computer graphics.

GeoGebra Commands & Parameters

Midpoint(A, B) → C
Vector(C, B) → u
OrthogonalVector(u) → v
CurveCartesian(((1 - t)^(3) * F) + (((3 * (1 - t)^(2)) * t) * U) + (((3 * (1 - t)) * t^(2)) * S) + (t^(3) * L), t, 0, 1) → a
Line(A, E) → g
Intersect(g, a) → M, N, O
LineBisector(A, B) → f
Polygon(A, F, M) → t1, m, a_1, f_1
Mirror(E, f) → E'
Mirror(O, f) → O'
Mirror(L, f) → L'
Mirror(D, f) → D'
CurveCartesian(((1 - t)^(3) * A) + (((3 * (1 - t)^(2)) * t) * W) + (((3 * (1 - t)) * t^(2)) * Q) + (t^(3) * E), t, 0, 1) → b
Mirror(b, f) → b'
Mirror(a, f) → a'
Mirror(A, f) → A'
Mirror(F, f) → F'
Mirror(M, f) → M'
Polygon(A', F', M') → t1', m', h, f'
Line(A, B) → i
Circle(R, Z) → c
Circle(R, B_1) → k
OrthogonalLine(A_1, i) → j
OrthogonalLine(Z, i) → n
Mirror(D_1, n) → E_1
Mirror(C_1, n) → F_1
Segment(D_1, C_1) → p
Midpoint(R, F_1) → G_1
CurveCartesian(((1 - t)^(3) * D_1) + (((3 * (1 - t)^(2)) * t) * L_1) + (((3 * (1 - t)) * t^(2)) * N_1) + (t^(3) * H_1), t, 0, 1) → q
Line(R, F_1) → s
Intersect(s, q) → O_1, P_1, Q_1
Segment(Q_1, F_1) → r
Polygon(L, D, E, S_1) → c1, l, t, d, e
Mirror(L, f) → L'_{1}
Mirror(D, f) → D'_{1}
Mirror(E, f) → E'_{1}
Mirror(N, f) → N'
Mirror(L, f) → L'_{2}
Mirror(D, f) → D'_{2}
Mirror(E, f) → E'_{2}
Mirror(S_1, f) → T_1
Polygon(L'_{2}, D'_{2}, E'_{2}, T_1) → c1', l'_{2}, d'_{2}, e'_{2}, t_1