learn-wgpu/assets/js/3.2a393c66.js

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We're finally going to use them. Normals represent the direction a surface is facing. By comparing the normal of a fragment with a vector pointing to a light source, we get a value of how light/dark that fragment should be. We compare the vector be using the dot product to get the cosine of the angle between them.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(218),alt:"./normal_diagram.png"}})]),t._v(" "),n("p",[t._v("If the dot product of the normal and light vector is 1.0, that means that the current fragment is directly inline with the light source and will receive the lights full intensity. 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This is wrong, but we'll fix it later.")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("void")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("main")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("{")]),t._v("\n    v_tex_coords "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" a_tex_coords"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("    v_normal "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" a_normal"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// NEW!")]),t._v("\n    "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec4")]),t._v(" model_space "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" model_matrix "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec4")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("a_position"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("1.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// NEW!")]),t._v("\n    v_position "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" model_space"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(".")]),t._v("xyz"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// NEW!")]),t._v("\n    gl_Position "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" u_view_proj "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" model_space"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// UPDATED!")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("}")]),t._v("\n")])])]),n("p",[t._v("Now in "),n("code",[t._v("shader.frag")]),t._v(" we'll take in the vertex's normal and position.")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("layout")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("location"),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("in")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec2")]),t._v(" v_tex_coords"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("layout")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("location"),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("1")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("in")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" v_normal"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// NEW!")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("layout")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("location"),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("2")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("in")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" v_position"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// NEW!")]),t._v("\n")])])]),n("p",[t._v("With that we can do the actual calculation. Below the "),n("code",[t._v("ambient_color")]),t._v(" calculation, but above "),n("code",[t._v("result")]),t._v(", add the following.")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" normal "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("normalize")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("v_normal"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" light_dir "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("normalize")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("light_position "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("-")]),t._v(" v_position"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("float")]),t._v(" diffuse_strength "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("max")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("dot")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("normal"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" light_dir"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("0.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" diffuse_color "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" light_color "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" diffuse_strength"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n")])])]),n("p",[t._v("Now we can include the "),n("code",[t._v("diffuse_color")]),t._v(" in the "),n("code",[t._v("result")]),t._v(".")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" result "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("ambient_color "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("+")]),t._v(" diffuse_color"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" object_color"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(".")]),t._v("xyz"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n")])])]),n("p",[t._v("With that we get something like this.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(219),alt:"./ambient_diffuse_wrong.png"}})]),t._v(" "),n("h2",{attrs:{id:"the-normal-matrix"}},[n("a",{staticClass:"header-anchor",attrs:{href:"#the-normal-matrix"}},[t._v("#")]),t._v(" The normal matrix")]),t._v(" "),n("p",[t._v("Remember when I said passing the vertex normal directly to the fragment shader was wrong? Let's explore that by removing all the cubes from the scene except one that will be rotated 180 degrees on the y-axis.")]),t._v(" "),n("div",{staticClass:"language-rust extra-class"},[n("pre",{pre:!0,attrs:{class:"language-rust"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("const")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token constant"}},[t._v("NUM_INSTANCES_PER_ROW")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(":")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("u32")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("1")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n\n"),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// In the loop we create the instances in")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("let")]),t._v(" rotation "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token namespace"}},[t._v("cgmath"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("::")])]),n("span",{pre:!0,attrs:{class:"token class-name"}},[t._v("Quaternion")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("::")]),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("from_axis_angle")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("0.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("1.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("0.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(".")]),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("into")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(",")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token namespace"}},[t._v("cgmath"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("::")])]),n("span",{pre:!0,attrs:{class:"token class-name"}},[t._v("Deg")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token number"}},[t._v("180.0")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n")])])]),n("p",[t._v("We'll also remove the "),n("code",[t._v("ambient_color")]),t._v(" from our lighting "),n("code",[t._v("result")]),t._v(".")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("vec3")]),t._v(" result "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("diffuse_color"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" object_color"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(".")]),t._v("xyz"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n")])])]),n("p",[t._v("That should give us something that looks like this.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(220),alt:"./diffuse_wrong.png"}})]),t._v(" "),n("p",[t._v("This is clearly wrong as the light is illuminating the wrong side of the cube. This is because we aren't rotating our normals with our object, so no matter what direction the object faces, the normals will always face the same way.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(221),alt:"./normal_not_rotated.png"}})]),t._v(" "),n("p",[t._v("We need to use the model matrix to transform the normals to be in the right direction. We only want the rotation data though. A normal represents a direction, and should be a unit vector throughout the calculation. We can get our normals into the right direction using what is called a normal matrix. We can calculate the normal matrix with the following.")]),t._v(" "),n("div",{staticClass:"language-glsl extra-class"},[n("pre",{pre:!0,attrs:{class:"language-glsl"}},[n("code",[n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// shader.vert")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("mat4")]),t._v(" model_matrix "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" model_matrix"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n"),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("mat3")]),t._v(" normal_matrix "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" "),n("span",{pre:!0,attrs:{class:"token keyword"}},[t._v("mat3")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("transpose")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),n("span",{pre:!0,attrs:{class:"token function"}},[t._v("inverse")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v("(")]),t._v("model_matrix"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(")")]),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\nv_normal "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("=")]),t._v(" normal_matrix "),n("span",{pre:!0,attrs:{class:"token operator"}},[t._v("*")]),t._v(" a_normal"),n("span",{pre:!0,attrs:{class:"token punctuation"}},[t._v(";")]),t._v("\n")])])]),n("p",[t._v("This takes the "),n("code",[t._v("model_matrix")]),t._v(" from our "),n("code",[t._v("instance_buffer")]),t._v(", inverts it, transposes it and then pulls out the top left 3x3 to just get the rotation data. This is all necessary because because normals are technically not vectors, there bivectors. The explanation is beyond me, but I do know that it means we have to treat them differently.")]),t._v(" "),n("ul",[n("li",[t._v("Note: I'm currently doing things in "),n("a",{attrs:{href:"https://gamedev.stackexchange.com/questions/65783/what-are-world-space-and-eye-space-in-game-development",target:"_blank",rel:"noopener noreferrer"}},[t._v("world space"),n("OutboundLink")],1),t._v(". Doing things in view-space also known as eye-space, is more standard as objects can have lighting issues when they are further away from the origin. If we wanted to use view-space, we would use something along the lines of "),n("code",[t._v("mat3(transpose(inverse(view_matrix * model_matrix)))")]),t._v(". Currently we are combining the view matrix and projection matrix before we draw, so we'd have to pass those in separately. 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This is rather expensive, so it is often suggested that you compute the "),n("code",[t._v("normal_matrix")]),t._v(" on the CPU and pass it in with the other uniforms.")])]),t._v(" "),n("p",[t._v("With that change our lighting now looks correct.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(222),alt:"./diffuse_right.png"}})]),t._v(" "),n("p",[t._v("Bringing back our other objects, and adding the ambient lighting gives us this.")]),t._v(" "),n("p",[n("img",{attrs:{src:a(223),alt:"./ambient_diffuse_lighting.png"}}),t._v(";")]),t._v(" "),n("h2",{attrs:{id:"specular-lighting"}},[n("a",{staticClass:"header-anchor",attrs:{href:"#specular-lighting"}},[t._v("#")]),t._v(" Specular Lighting")]),t._v(" "),n("p",[t._v("Specular lighting describes the highlights that appear on objects when viewed from certain angles. If you've ever looked at a car, it's the super bright parts. Basically, some of the light can reflect of the surface like a mirror. 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We're using Point3 for the camera.eye, and this is")]),t._v("\n        "),n("span",{pre:!0,attrs:{class:"token comment"}},[t._v("// the easiest way to convert to Vector4. 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