I am not sure how to make this formula work...

Let’s say we had a very weird two dimensional, sinusoidal topography such that z = f(x) = sinx with z the height and x is the distance from some marker. The slope in the x direction

I am trying to convert the scalar field (height versus position) to a vector field (direction and magnitude of greatest slope) mathematically

Thanks for the reply.

Here is what the article says....

We often wish to differentiate a function along three orthogonal axes. For example, imagine we know the topography of a ski area (see Figure A.6). For every location (in say, X and Y coordinates), we know the height above sea level. This is a scalar function. Now imagine we want to build a ski resort, so we need to know the direction of steepest descent and the slope (red arrows in Figure A.6).

To convert the scalar field (height versus position) to a vector field (direction and magnitude of greatest slope) mathematically, we would simply differentiate the topography function. Let’s say we had a very weird two dimensional, sinusoidal topography such that z = f(x) = sinx with z the height and x is the distance from some marker. The slope in the x direction (), then would be d _ dxf(x). If f(x,y,z) were a three dimentional topography then the gradient of the topography function would be:

So from the looks of it yes, a Gradient...

So lets say we have (x,y) as (10, 100)

then

z=sin(x);??

as for that I am not sure what comes after the cosine()....

Thanks!

That helps Alvaro, but why is cos(10),0 and not cos(10), 100??

so with a x,y pair of 10,100

the result xyz vector would be??

x,y, z= (cos(10), 100, sin(10)?

So is this correct then?

double Gradient(const std::vector<double> &v)
{
return sin(v[0]) + 2 * cos(v[1]) - sin(v[2]);
} std::vector<double> v;
v.push_back(1);
v.push_back(1);
v.push_back(1);
std::cout << Gradient(v) << std::endl; //result = 1.0806

but aren't I looking for these values?

     x(0) = 1.570795457
     x(1) = 6.423712373e-006
     x(2) = 4.712391906

If so how do I get to that result?

#include <iostream>
#include <cmath>

struct Vector3D {
  double x, y, z;

  Vector3D(double x, double y, double z) : x(x), y(y), z(z) {
  }
};

std::ostream &operator<<(std::ostream &os, Vector3D v) {
  return os << '(' << v.x << ',' << v.y << ',' << v.z << ')';
}

double f(Vector3D v) {
  return std::sin(v.x) + std::cos(v.y);
}

Vector3D Gradient(Vector3D v) {
  return Vector3D(std::cos(v.x), -std::sin(v.y), 0.0);
}

int main() {
  Vector3D v(1.0, 1.0, 1.0);

  std::cout << Gradient(v) << std::endl;
}

I am trying to calculate the slope of a point given X,Y coordinates... HTH you help me :)