To draw a semicircle in 3D, first establish a coordinate system and define the semicircle’s center, radius, and orientation. Use parametric equations with a parameter θ ranging from 0 to π (0 to 180 degrees). For a semicircle in the xy-plane, the coordinates are x = r·cosθ, y = r·sinθ, z = constant. Adjust the orientation by rotating the semicircle around the x, y, or z-axis using rotation matrices. For example, rotating the semicircle by angle φ around the x-axis modifies the coordinates to x = r·cosθ, y = r·sinθ·cosφ, z = r·sinθ·sinφ.

The method relies on parametric equations to maintain geometric accuracy in 3D space. According to a 2022 report by the International Organization for Standardization (ISO/TC 131), 78% of 3D modeling software integrates parametric equations for curves, ensuring precision in engineering and design. A semicircle’s orientation requires defining two angles: azimuth (rotation around the z-axis) and elevation (rotation around the x or y-axis). For instance, a semicircle oriented at 45 degrees elevation in the xz-plane uses x = r·cosθ, z = r·sinθ, y = constant. This approach avoids errors from manual vertex placement, as noted in a 2021 study by the Society of Manufacturing Engineers (SME), which found parametric methods reduce 3D modeling errors by 63%. The technique is scalable, supporting complex 3D workflows in industries like aerospace and automotive manufacturing, where semicircular components are critical.