Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes.

保形几何代数（CGA）提供了几何图元和保形变换的统一表示，因此在计算机图形学领域具有重要的前景。在本文中，我们将使用Blinn-Phong照明模型在CGA中实现一个简单的光线跟踪器，然后将其用于检查与由几何图元直接插值生成的曲面的光线交点。由这些插值形成的普通曲面将使用解析法线进行渲染。此外，还介绍并绘制了点对插值的特殊情况，这些情况可能会在图形应用程序中使用。对于标量参数的标量加4向量元素的平方根的导数，找到了一个封闭形式的表达式。该平方根导数用于构造投影到叶片歧管的纯级多矢量的导数的表达式。叶片歧管投影提供了一种用于找到插值曲面的法线的分析方法，其用法在光线跟踪器的光照计算中以及在生成顶点法线以将演化的表面导出为多边形网格时得到了展示。