In general, most 3D parametric design systems use plane and sphere as basic tools to draw a three-dimensional diagram. In this paper, we introduce a class of new drawing tools: conicoid. The scope of three-dimensional diagram that can be drawn with conicoid is strictly larger than that with plane and sphere only. We prove that a diagram can be drawn with conicoid sequentially if and only if it can be described by a set of triangular equations of degree less than nine. Spatial Appolonius drawing problems can be completely solved with conicoid.