Arcball camera behaving oddly - c++

Question

I am a bit confused. I need help, I tried implementing an arcball camera. The theory I followed is here:
https://www.khronos.org/opengl/wiki/Object_Mouse_Trackball
It "works" except it doesn;t behave like the arcball camera in Renderdoc:
Mine:
Renderdoc
So in mine when you try to rotate too far away from the screen center the rotation seems to be on the opposite direction of where it should be
vec3 ScreenToArcSurface(vec2 pos)
{
const float radius = 0.9f; // Controls the speed
if(pos.x * pos.x + pos.y * pos.y >= (radius * radius) / 2.f - 0.00001)
{
// This is equal to (r^2 / 2) / (sqrt(x^2 + y^2)) since the magnitude of the
// vector is sqrt(x^2 + y^2)
return {pos, (radius * radius / 2.f) / (length(pos))};
}
return {pos.x, pos.y, sqrt(radius * radius - (pos.x * pos.x + pos.y * pos.y))};
}
void ArcballCamera::UpdateCameraAngles(void* ptr, glm::vec2 position, glm::vec2 offset)
{
auto camera = reinterpret_cast<ArcballCamera*>(ptr);
vec3 vb = ScreenToArcSurface(position);
vec3 va = ScreenToArcSurface(position - offset);
float angle = acos(glm::min(1.f, dot(vb, va)));
vec3 axis = cross(va, vb);
camera->rotation *= quat(cos(angle) / 2.f, sin(angle) * axis);
camera->rotation = normalize(camera->rotation);
}
glm::mat4 ArcballCamera::GetViewMatrix()
{
return glm::lookAt(
look_at_point + rotation * (position - look_at_point),
look_at_point,
rotation * up);
}
I don't understand what difference there is between what I implemented and what the khronos link is describing.
I fixed it by multiplying the position by -1;.
I don't understand why this fixes the math. The input coorindates are what i expect. the poisition is normalized from -1 to 1 and top left is (-,-) top right is (+,-), bottom left (-,+) and finally the last one is (+,+).
So I don;t know Why I need to work in a negated coordinate system for this to work.

Answer 1

The problem is that the Website I took this from defined the formula for the OpenGL coordinate system.
However I am working on vulkan, where the Y coordinate is flipped, which changes the handedness of the system. Due to this, using the formula as is uses the wrong half of the sphere.
The correct implementation for Vulkan just needs to negate the z component, i.e:
vec3 ScreenToArcSurface(vec2 pos)
{
const float radius = 0.9f; // Controls the speed
if(pos.x * pos.x + pos.y * pos.y >= (radius * radius) / 2.f - 0.00001)
{
// This is equal to (r^2 / 2) / (sqrt(x^2 + y^2)) since the magnitude of the
// vector is sqrt(x^2 + y^2)
return {pos, -(radius * radius / 2.f) / (length(pos))};
}
return {pos.x, pos.y, -sqrt(radius * radius - (pos.x * pos.x + pos.y * pos.y))};
}