Here, I will use an example ridge that I have made and tested in XF to demonstrate how the curved part of the ridges slope in.
Here is a figure that represents one of these ridges. We are viewing it directly at the edge of the ridge, so the blue line actually represents the side. The purple curve should lie directly aligned with the blue line but doesn’t. The same goes for the green line and orange/red lines (which do lie in the same plane, but that plane isn’t aligned with the other side) below, which is the other side of the ridge.

x0=4; y0=4;z0=0; yf=6; H=30; zf=30; xf=zf; β=2;τ=0.26;

ParametricPlot3D[{
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(xf-x0)/τ*t,y0,z0},
{x0+(xf-x0)/τ*t,-y0,z0},
{xf+xf/τ*t,yf,zf},
{xf+xf/τ*t,-yf,zf},
{xf+zf/τ*t,y0+(yf-y0)/τ*t,zf/τ*t},
{xf+zf/τ*t,-y0-(yf-y0)/τ*t,zf/τ*t},
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,β*Log[t/τ*(Exp[zf/β]-1)+1]},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,β*Log[t/τ*(Exp[zf/β]-1)+1]}
},{t,0,τ}]

To check if our assumption that the curve lies in a single plane at all, we need to check the torsion. See here: https://en.wikipedia.org/wiki/Torsion_of_a_curve#:~:text=In%20the%20differential%20geometry%20of,curvature%20of%20a%20plane%20curve. 

The important thing to check is that the numerator gives zero (but without the cross section being zero). Here, I show that the numerator is indeed zero (and it’s clear why by differentiating r and r’ twice).

zf=.;β=.;τ=.;x0=.; y0=.;yf=.;xf=.;z0=.;
x[t_,x0_,xf_,τ_]=x0+(xf-x0)/τ*t;
y[t_,y0_,yf_,τ_]=y0+(yf-y0)/τ*t;
z[t_,z0_,zf_,β_,τ_]=β*Log[t/τ*(Exp[zf/β]-1)+1];
r[t_,x0_,y0_,z0_,xf_,yf_,zf_,β_,τ_]={x[t,x0,xf,τ],y[t,y0,yf,τ],z[t,z0,zf,β,τ]};
rp[t_,x0_,y0_,z0_,xf_,yf_,zf_,β_,τ_]=FullSimplify[D[r[t,x0,y0,z0,xf,yf,zf,β,τ],t]]
rp2[t_,x0_,y0_,z0_,xf_,yf_,zf_,β_,τ_]=FullSimplify[D[rp[t,x0,y0,z0,xf,yf,zf,β,τ],t]]
rp3[t_,x0_,y0_,z0_,xf_,yf_,zf_,β_,τ_]=FullSimplify[D[rp2[t,x0,y0,z0,xf,yf,zf,β,τ],t]]
(*Get the cross product of r' and r'' and dot it with r'''*)
Cross[rp[t,x0,y0,z0,xf,yf,zf,β,τ],rp2[t,x0,y0,z0,xf,yf,zf,β,τ]].rp3[t,x0,y0,z0,xf,yf,zf,β,τ]

Anything below is just me playing around trying other functions or tests of the curvature.

ParametricPlot3D[{
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(xf-x0)/τ*t,y0,z0},
{x0+(xf-x0)/τ*t,-y0,z0},
{xf+xf/τ*t,yf,zf},
{xf+xf/τ*t,-yf,zf},
{xf+zf/τ*t,y0+(yf-y0)/τ*t,zf/τ*t},
{xf+zf/τ*t,-y0-(yf-y0)/τ*t,zf/τ*t},
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,Sqrt[zf]*Sqrt[z0+(zf-z0)*t/τ]},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,Sqrt[zf]*Sqrt[z0+(zf-z0)*t/τ]}
},{t,0,τ}]

ParametricPlot3D[{
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(xf-x0)/τ*t,y0,z0},
{x0+(xf-x0)/τ*t,-y0,z0},
{xf+xf/τ*t,yf,zf},
{xf+xf/τ*t,-yf,zf},
{xf+zf/τ*t,y0+(yf-y0)/τ*t,zf/τ*t},
{xf+zf/τ*t,-y0-(yf-y0)/τ*t,zf/τ*t},
(*{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,zf^(5/6)*(z0+(zf-z0)*t/τ)^(1/6)},*)
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,zf^(5/6)*(z0+(zf-z0)*t/τ)^(1/6)},
{xf^(1/2)*(x0+(xf-x0)*t/τ)^(1/2)+(Sqrt[xf*x0]-x0)*(t-τ)/τ,yf^(1/2)*(y0+(yf-y0)*t/τ)^(1/2)+(Sqrt[yf*y0]-y0)*(t-τ)/τ,zf^(1/2)*(z0+(zf-z0)*t/τ)^(1/2)}
},{t,0,τ}]

f[x_]=x

x[t_]=x0+(zf-x0)/τ*t

D[x[t],t]

B={x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t};
i={x0+(xf-x0)/τ*t,y0,z0};
L={x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t};
n1=Cross[B,i];
n2=Cross[i,L];
n1-n2

x0=4; y0=4;z0=0; yf=6; H=30; zf=30; xf=zf; β=2;τ=0.26;
i=.;B=.;L=.;
i={x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t};
B={x0+(xf-x0)/τ*t,y0,z0};
L[t_]={x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,β*Log[t/τ*(Exp[zf/β]-1)+1]};
Lnew=L[t]+(Cross[B,i]+Cross[i,L[t]])
ParametricPlot3D[{
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,(zf-z0)/τ*t},
{x0+(xf-x0)/τ*t,y0,z0},
{x0+(xf-x0)/τ*t,-y0,z0},
{xf+xf/τ*t,yf,zf},
{xf+xf/τ*t,-yf,zf},
{xf+zf/τ*t,y0+(yf-y0)/τ*t,zf/τ*t},
{xf+zf/τ*t,-y0-(yf-y0)/τ*t,zf/τ*t},
{x0+(zf-x0)/τ*t,y0+(yf-y0)/τ*t,β*Log[t/τ*(Exp[zf/β]-1)+1]},
{x0+(zf-x0)/τ*t,-y0-(yf-y0)/τ*t,β*Log[t/τ*(Exp[zf/β]-1)+1]},
Lnew
},{t,0,τ}]

Cross[B,I]

I