$\nabla f$

Mehr Höhenlinien durch Ziehen von k.

refresh Strg f

A = (-0.4538271604938277, -0.4733333333333329, 0)
f(x, y) = (ℯ^(((-((x + 1)^(2) + (y + 0.5)^(2)))) / 0.5) * 2) + ℯ^(((-((x - 0.5)^(2) + y^(2)))) / 0.5)
A_w: (x(A), y(A), f(x(A), y(A)))
fx = Derivative(f(x, y), x)
fy = Derivative(f(x, y), y)
Nablaf = Vector((x(A_w), y(A_w), 0), (x(A_w) + fx(x(A_w), y(A_w)), y(A_w) + fy(x(A_w), y(A_w)), 0))
Nablaf_w = Vector((x(A_w), y(A_w), z(A_w)), (x(A_w) + fx(x(A_w), y(A_w)), y(A_w) + fy(x(A_w), y(A_w)), z(A_w)))
m: ((fx(x(A_w), y(A_w)))^(2) + (fy(x(A_w), y(A_w)))^(2))^(1 / 2)
w = Vector((x(A_w), y(A_w), z(A_w)), (x(A_w) + fx(x(A_w), y(A_w)) / m, y(A_w) + fy(x(A_w), y(A_w)) / m, z(A_w) + ((fx(x(A_w), y(A_w)))^(2) + (fy(x(A_w), y(A_w)))^(2)) / m))
C = (-0.7422222222222221, -1.5716049382716046)
D = (-0.5960493827160492, -1.2358024691358023)
S = (-0.28, -0.8802469135802468)
F = (0.02814814814814861, -0.4338271604938271)
M = (0.47456790123456855, -0.35481481481481475)
H = (0.7313580246913588, -0.3864197530864197)
I = (0.9249382716049391, -0.7380246913580245)
g = Spline({C, D, S, F, M, H, I}, 3)
J: (x(C), y(C), f(x(C), y(C)))
K: (x(D), y(D), f(x(D), y(D)))
xg(t) = x(g(t))
yg(t) = y(g(t))
wander = CurveCartesian(xg(t), yg(t), f(xg(t), yg(t)), t, 0, 1)
S_{w}: (x(S), y(S), f(x(S), y(S)))
M_w: (x(M), y(M), f(x(M), y(M)))
O = (-2.4266666666666685, -1.7792592592592593)
P = (-2.0266666666666686, -1.7792592592592593)
k = 0.8 (slider from 0 to 2, step 0.2)
Eb_k = Plane(z = k)
hoe_w = IntersectPath(Eb_k, f)
hoe_k: k = f(x, y)