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I've seen the term Normal being used in many places, but I'm not quite sure what it is or what it's used for; what exactly are they?

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Normals are vectors that are Orthogonal to the Tangent plane of a curved surface; Or simply orthogonal to a face.

The Normals are usually used to determine a surface's orientation toward a light source for shading. Most common examples:

  • Flat, Goraud, Phong shading

    enter image description here

  • Fresnel, Refraction, Reflection effects

  • Bump, Normal, Displacement mapping

Normals are generally normalized to length 1 (in arbitrary units), otherwise calculation errors, and thus artifacts, may arise. Since they only point one way they are also used for back visibility culling (when double-sided is off).

That's why it is important for the normals to be consistent and coherent (i.e. point in the correct way - outwards of a model).

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    $\begingroup$ Normals are also used for bump and (duh) normal mapping and smooth shading. $\endgroup$
    – PGmath
    Dec 20, 2014 at 18:42
  • $\begingroup$ @PGmath well, yeah... Those were just some examples. $\endgroup$ Dec 20, 2014 at 18:44
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    $\begingroup$ @NoviceInDisguise Yea, it felt kind of dumb saying that normal maps mess with normals. But then again, when I first saw a normal map I thought “that doesn't look very normal to me!” $\endgroup$
    – PGmath
    Dec 20, 2014 at 20:35
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Besides the mathematical explanations, I think a picture will help to understand what is meant by normals and perpendicular. The faces having a normal (blue lines) pointing to a light source are rendered brighter than the faces pointing into other directions.

enter image description here

You can toggle the display of normals in the Properties Panel (right panel N):

enter image description here

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    $\begingroup$ +1 if you also add screenshot showing how you turn on the normal lines display. $\endgroup$
    – Neil
    Dec 22, 2014 at 8:38

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