Is a Heightfield a Scalar or a Vector and How Many Dimensions Does it Have?

In summary, a heightfield can be described as a function h=h(x,y) where for each set of values x and y, there is a corresponding scalar height h. This means that a heightfield is a 2-Dimensional surface in a 3-Dimensional space.
  • #1
hexa
34
0
Hello,

I've been wondering if a heightfield is a scalar or a vector, and how many dimensions in space it has.

Sure, if it's a scalar it only has a magnitude, and as a vector magnitude and direction but I cannot see either, or keep them apart in this case. Density or gravityacceleration are easier I guess.

Dimensions: 2 would work out: h=(x,y) but would 1d and 3d possible as well?
Hexa
 
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  • #2
Hello Hexa,

in the case of h=h(x,y) you get for each set of values x and y a corresponding height h, which is a scalar. Or to put it another way: For every point on the x-y-surface you get a certain height h. So altogether the function describes a 2-Dimensional surface in a 3-Dimensional space.

I hope that was helpful for you.
 
  • #3
Hi David,

that was also my intuition. I got confused by an old exam question about visualising such heightfield as vectorfield:confused: and could not find a direction.

Thanks a lot

Hexa

DavidBektas said:
Hello Hexa,

in the case of h=h(x,y) you get for each set of values x and y a corresponding height h, which is a scalar. Or to put it another way: For every point on the x-y-surface you get a certain height h. So altogether the function describes a 2-Dimensional surface in a 3-Dimensional space.

I hope that was helpful for you.
 

1. What is the difference between scalar and vector quantities?

Scalar quantities have only magnitude, while vector quantities have both magnitude and direction.

2. How are scalar and vector quantities represented?

Scalar quantities are represented by a single number or value, while vector quantities are represented by a magnitude and direction, often using an arrow or bold font.

3. What are some examples of scalar quantities?

Some examples of scalar quantities include distance, speed, temperature, and mass.

4. What are some examples of vector quantities?

Examples of vector quantities include displacement, velocity, force, and acceleration.

5. How do you add and subtract scalar and vector quantities?

Scalar quantities can be added or subtracted by simply adding or subtracting their numerical values. Vector quantities can be added or subtracted using vector addition or subtraction, taking into account both magnitude and direction.

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