learn-wgpu/assets/js/4.1a5062fd.js

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Let's compare our results with the last tutorial.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(229),alt:""}}),t._v(" "),n("img",{attrs:{src:a(230),alt:""}})]),t._v(" "),n("p",[t._v("Parts of the scene are dark when they should be lit up, and vice versa.")]),t._v(" "),n("h2",{attrs:{id:"tangent-space-to-world-space"}},[n("a",{staticClass:"header-anchor",attrs:{href:"#tangent-space-to-world-space"}},[t._v("#")]),t._v(" Tangent Space to World Space")]),t._v(" "),n("p",[t._v("I mentioned it briefly in the "),n("RouterLink",{attrs:{to:"/intermediate/tutorial10-lighting/#the-normal-matrix"}},[t._v("lighting tutorial")]),t._v(', that we were doing our lighting calculation in "world space". This meant that the entire scene was oriented with respect to the '),n("em",[t._v("world's")]),t._v(" coordinate system. When we pull the normal data from our normal texture, all the normals are in what's known as  pointing roughly in the positive z direction. 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We're then going to use that to transform our normal map data to be in world space.")]),t._v(" "),n("h2",{attrs:{id:"the-tangent-and-the-bitangent"}},[n("a",{staticClass:"header-anchor",attrs:{href:"#the-tangent-and-the-bitangent"}},[t._v("#")]),t._v(" The tangent, and the bitangent")]),t._v(" "),n("p",[t._v("We have one of the 3 vectors we need, the normal. What about the others? These are the tangent, and bitangent vectors. A tangent represents any vector that is parallel with a surface (aka. doesn't intersect with it). The tangent is always perpendicular to the normal vector. The bitangent is a tangent vector that is perpendicular to the other tangent vector. Together the tangent, bitangent, and normal represent the x, y, and z axes respectively.")]),t._v(" "),n("p",[t._v("Some model formats include the tanget and bitangent (sometimes called the binormal) in the vertex data, but OBJ does not. We'll have to calculate them manually. Luckily we can derive our tangent, and bitangent from our existing vertex data. Take a look at the following diagram.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(231),alt:""}})]),t._v(" "),n("p",[t._v("Basically we can use the edges of our triangles, and our normal to calculate the tangent and bitangent. 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The fragment shader gets run for "),n("strong",[t._v("every pixel")]),t._v(". To say this is inefficient is an understatement. Even so, we can't do the transformation in the vertex shader since we need to sample the normal map in the pixel shader. If want to use the "),n("code",[t._v("tangent_matrix")]),t._v(" out of the fragment shader, we're going to have to think outside the box.")]),t._v(" "),n("h2",{attrs:{id:"world-space-to-tangent-space"}},[n("a",{staticClass:"header-anchor",attrs:{href:"#world-space-to-tangent-space"}},[t._v("#")]),t._v(" World Space to Tangent Space")]),t._v(" "),n("p",[t._v("The variables we're using in the lighting calculation are "),n("code",[t._v("v_position")]),t._v(", "),n("code",[t._v("light_position")]),t._v(", and "),n("code",[t._v("u_view_position")]),t._v(". These are in "),n("code",[t._v("world space")]),t._v(" while our normals are in "),n("code",[t._v("tangent space")]),t._v(". We can convert from "),n("code",[t._v("world space")]),t._v(" to "),n("code",[t._v("tangent space")]),t._v(" by multiplying by the inverse of the "),n("code",[t._v("tangent_matrix")]),t._v(". 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