I didn't understand what distance function is at that time. Is the distance function from this article talking about the same thing? And if it is, how to visualize f(x) in this form
https://www.sciencedirect.com/topics/engineering/distance-function
chenj
I am also very confused by the slide in general. I think I understand the blending part as the pictures show, but I don't understand how we related the pictures with combining distance functions.
motoole2
@tplatina Your link refers to something different.
As defined on this slide, "a distance function gives distance to closest point on object". Let's consider a distance function for the unit sphere, which is given by f(x) = sqrt(x^2 + y^2 + z^2) - 1. Any point on the surface of the sphere produces a value of 0. For a point x outside of the sphere, f(x) produces the shortest distance between x and some point on the sphere, and is strictly larger than zero. So if I want to visualize the sphere, I can draw all points x where f(x) <= 0, representing points on or inside the object.
Also, try working through exactly why `f(x) = min(d_1(x),d_2(x)) is the Boolean union of two distance functions.
The blending equation in the middle of the slide is chosen a bit arbitrarily in my opinion. It's an example of just one of many ways to combine two distance functions to blend the two shapes they represent.
I didn't understand what distance function is at that time. Is the distance function from this article talking about the same thing? And if it is, how to visualize f(x) in this form https://www.sciencedirect.com/topics/engineering/distance-function
I am also very confused by the slide in general. I think I understand the blending part as the pictures show, but I don't understand how we related the pictures with combining distance functions.
@tplatina Your link refers to something different.
As defined on this slide, "a distance function gives distance to closest point on object". Let's consider a distance function for the unit sphere, which is given by
f(x) = sqrt(x^2 + y^2 + z^2) - 1. Any point on the surface of the sphere produces a value of 0. For a pointxoutside of the sphere,f(x)produces the shortest distance betweenxand some point on the sphere, and is strictly larger than zero. So if I want to visualize the sphere, I can draw all pointsxwheref(x) <= 0, representing points on or inside the object.Also, try working through exactly why `f(x) = min(d_1(x),d_2(x)) is the Boolean union of two distance functions.
The blending equation in the middle of the slide is chosen a bit arbitrarily in my opinion. It's an example of just one of many ways to combine two distance functions to blend the two shapes they represent.