My raw primitives cannot be displayed in Raymarching

Question

I encountered a very strange problem while learning Raymarching. My equation cannot be displayed well. It can be displayed well in matlab. But it can't be shown on Shadertoy at all.

My equation：

f(x,y,z) = (x^2+y^2+z^2)^2+2*y*(x^2+y^2+z^2)+2*(x^2+z^2);

code in matlab:

f =@(x,y,z) (x.^2+y.^2+z.^2)^2+2*y*(x.^2+y.^2+z.^2)+2*(x.^2+z.^2);
fimplicit3(f)

matlab displays a normal picture

code in shadertoy：

float sdRound(vec3 p)
{
   float lengthXYZ = (p.x * p.x+p.y * p.y+p.z * p.z); 
   return lengthXYZ * lengthXYZ+2.0 * p.y * lengthXYZ+2.0 * (p.x * p.x+p.z * p.z);
}

I learned, practiced, and modified the iq code. (https://www.shadertoy.com/view/Xds3zN).

But it cannot be displayed normally. Shadertoy displays abnormal pictures Shadertoy displays abnormal pictures

I don't know where the problem occurred. Please help me. Has troubled me for a long time.

Forgive my poor English. I use Google Translate.

score 0 · Answer 1 · answered Feb 09 '22 at 15:40

Your problem seems to lay in the very understanding of what raymarching is.
Your formula mathematically describes a surface (that is why it is displayed nicely in matlab), but this is not how raymarching works.
Defining an object for raymarching means defining a distance function for your object (which is different from a function mathematically describing its surface). These functions are identical for zero-returned values (which means coordinates are on the surface), but they are different for other values.
To create something similar to your object, I would suggest to explore the sdRoundCone method from iq's Raymarching primitives, as it seems the closest to what you want to achieve.

My raw primitives cannot be displayed in Raymarching

1 Answers1