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normal map question

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Hi, I hope this is a simple one for you math gurus: I have a (BRDF) shader and now I want to add bump-mapping. So, the casual normal has to be replaced with a value from the normalmap: newNormal = 2 * tex2D( normalMap, uv ) - 1 The problem is that this 'newNormal' is different than the usual normal passed by the object itself. Normally (without bumpmapping) I do something like this: vertex shader
	  	oEye 	= normalize(eyePos   - iPos.xyz);
		oLight 	= normalize(lightPos - iPos.xyz);
        float3	h	= normalize( oLight + oEye );
		oV.xyz	= float3(
   				  dot(h,iTangent),
			          dot(h,iBiNrm	),
			          dot(h,iNormal	) // <---
			        );
This 'oV' vector is used in the pixel shader for the BRDF stuff. Anyway, that "dot( h,iNormal)" part should be replaced with the normal from the bumpmap. But how? pixel shader
  newNormal = 2 * tex2D( normalMap, uv ) - 1;
  oV.z = ...?
Note that the normals on the map are local (they all point towards +Z so you have that blue/purple map). Greetings, Rick

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