Step 5: if the ray intersects an object, compute the color of that object at the intersection point and add this result to a temporary variable.Step 4: trace a ray in the scene in the sampled direction.Step 3: transform the sample direction from the original coordinate system to the shaded point coordinate system.We will show in this chapter how this can be done in practice. Step2: create a sample using the spherical to Cartesian coordinates equations.Step 1: create a Cartesian coordinate system in which the up vector is oriented along the shaded point normal \(N\) (the shaded point normal \(N\) and the up vector of the coordinate system are aligned).We shouldn't also forget to multiply the object's color by the cosine of the angle between the shading normal and the ray direction (which in this case can be seen the light direction). Monte Carlo theory also implies to divide each sample by the random variable PDF. All the colors are summed up and divided by the number N of cast samples.
If these rays hit an object, the color at the intersection point is computed and returned to the shading point. Rays are randomly generated into a hemisphere of directions oriented around the shading normal \(N\). If you read the lesson on Geometry, you should know that once we have the axes of an orthogonal coordinate system \(C\), we can transform any point or vector (aka direction) from any Cartesian coordinate system to \(C\).įigure 2: the principle of Monte Carlo integration applied to a 3D scene.
#Source engine sdk light rays how to#
We will explained in this lesson how samples are created, how to create a new coordinate system in which the shading normal \(N\) defines the up axis of that coordinate system, and how the other axis of that local Cartesian coordinate system (which are technically tangent to the surface at \(P\) and perpendicular to \(N\)) are also computed. The reason why we prefer to create samples in a hemisphere whose up vector is oriented with the y-axis of the world Cartesian coordinate system, is because the coordinates of the sample in this coordinate system can be easily computed with the basic spherical-to-Cartesian coordinates equations, which we know are:Īnd then transformed in the shaded point local coordinate system. Though as in the 2D case, it is easier to create these samples in a hemisphere oriented with the y-axis of some "canonical" Cartesian coordinate systems and then transform then into the shaded point local coordinate system (in which the hemisphere is oriented along the normal as shown in figure 1 - bottom). Figure 1: transforming sampling from the coordinate system in which they were created to world space (in the shaded point local coordinate system whose up vector is aligned with \(N\)).Ĭoncept: ideally we want to create samples on the hemisphere oriented about the normal \(N\) of the shaded point \(P\).
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