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diff --git a/futatabi/equations.vert b/futatabi/equations.vert
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+++ b/futatabi/equations.vert
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+#version 450 core
+#extension GL_ARB_shader_viewport_layer_array : require
+
+layout(location=0) in vec2 position;
+out vec3 tc0, tc_left0, tc_down0;
+out vec3 tc1, tc_left1, tc_down1;
+out float line_offset;
+
+uniform sampler2DArray diffusivity_tex;
+
+void main()
+{
+	// The result of glOrtho(0.0, 1.0, 0.0, 1.0, 0.0, 1.0) is:
+	//
+	//   2.000  0.000  0.000 -1.000
+	//   0.000  2.000  0.000 -1.000
+	//   0.000  0.000 -2.000 -1.000
+	//   0.000  0.000  0.000  1.000
+	gl_Position = vec4(2.0 * position.x - 1.0, 2.0 * position.y - 1.0, -1.0, 1.0);
+	gl_Layer = gl_InstanceID;
+
+	const vec2 half_texel = 0.5f / textureSize(diffusivity_tex, 0).xy;
+
+	vec2 tc = position;
+	vec2 tc_left = vec2(tc.x - half_texel.x, tc.y);
+	vec2 tc_down = vec2(tc.x, tc.y - half_texel.y);
+
+	// Adjust for different texel centers.
+	tc0 = vec3(tc.x - half_texel.x, tc.y, gl_InstanceID);
+	tc_left0 = vec3(tc_left.x - half_texel.x, tc_left.y, gl_InstanceID);
+	tc_down0 = vec3(tc_down.x - half_texel.x, tc_down.y, gl_InstanceID);
+
+	tc1 = vec3(tc.x + half_texel.x, tc.y, gl_InstanceID);
+	tc_left1 = vec3(tc_left.x + half_texel.x, tc_left.y, gl_InstanceID);
+	tc_down1 = vec3(tc_down.x + half_texel.x, tc_down.y, gl_InstanceID);
+
+	line_offset = position.y * textureSize(diffusivity_tex, 0).y - 0.5f;
+}