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Simplex Noise Normals

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I've implemented simplex noise in HLSL and used it alongside fBm to procedurally generate a basic terrain. Now I'd also like to generate normals for the terrain but I can't think of a way of doing this. I tried generating per face normals in the geometry shader but the terrain looked really unsmooth and one could see differences between the triangles quite easily. When I searched online, what I found was people talking about using the neighbouring values of the center point for which you want to find the normal for. However, I can't figure out how I would go about implementing this.

Currently, my geometry shader passes the SV_POSITION and the position in camera space along to the pixel shader (so I could do my lighting calculations in camera space). I use the camera space position to get the normal in camera space as well and then use basic Phong lighting calculations. However, the results look bad.

Here's my current normal calculation:
float3 CalculateNormal(float4 position) {
	float4 center = position;

	// find the vector along the x-axis
	float4 a1 = center - float4(1.0f, 0.0f, 0.0f, 0.0f);
	float4 a2 = center + float4(1.0f, 0.0f, 0.0f, 0.0f);

	a1.y = FractionalBrownianMotion(a1);
	a2.y = FractionalBrownianMotion(a2);

	float3 a = a2.xyz - a1.xyz;

	// find the vector along the z-axis
	float4 b1 = center - float4(0.0f, 0.0f, 1.0f, 0.0f);
	float4 b2 = center + float4(0.0f, 0.0f, 1.0f, 0.0f);

	b1.y = FractionalBrownianMotion(b1);
	b2.y = FractionalBrownianMotion(b2);

	float3 b = b2.xyz - b1.xyz;

	// find the normal
	float3 normal = cross(b, a);
	normal = normalize(normal);

	return normal;
And the result (note the black blobs, they move around as the camera moves too): http://postimg.org/image/blz98fdsb/

My normal calculations are obviously wrong but I don't know how to fix this. Hope you guys can help me out.

Thanks in advance!

EDIT: To not bump the thread up (but to still let people who might stumble onto this thread know): the above function works fine, I had issues with my coordinate spaces instead >.< Edited by dr4cula

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