几何约束求解广泛应用于机械设计，化学分子形成，几何定理证明和勘探等诸多领域，用于求解几何约束问题主要有3种方法：数值方法，符号方法和构造法，构造法用于具有简单易行的特点，因此被大多数的参数化机械设计系统作为求解几何约束问题的基本方法，针对构造法中只采用直线和圆，即直尺和圆规，来作为基本的作图工具，引进了一种新的作图工具，圆锥曲线，并且证明了在引进圆锥曲线以后，作图的范围明显大于只用直尺和圆规作图的范围；证明了一个图形能用圆锥曲线作出的充分必要条件是这个图形可以用一个三角化的次数小于等于4的方程组来描述；由于三次和四次方程的解可以显式地表示出来，所以引进圆锥曲线作为一个新的作图工具仍然可以保持原来尺规作图的简洁性和完整性。

Geometric constraint solving has applications in a wide variety of fields, such as mechanical engineering, chemical molecular conformation, geometric theorem proving, and surveying. There are mainly three approaches to geometric constraint solving: numerical approach, symbolic approach and constructive approach. Since the constructive approach are simple and practicable, most parametric design take the constructive approach as the basic approach. In the light of the shortage of using only line and circle (rule and compass) as basic drawing tools in constructive approach, in this paper, we introduce a class of new drawing tools: conics. We prove that the class of diagrams within the drawing scope of this new tool is larger than that can be drawn with line and circle. Actually, we prove that a diagram can be drawn with conics if and only if this diagram can be described with a sequence of triangulated equations of degree less than or equal to four. This allows us to maintain the elegance of geometric constraint solving with ruler and compass, because the solutions of cubic and quartic equations can be written explicitly with radicals.