Envelope Interface: Definition, Geometric Properties, and Physical Significance

The Envelope Interface is defined as a composite geometric structure formed by connecting multiple segments of Survey Line Spirals in sequence. In the general case, the segments may have varying growth rates and angular spans, producing a wide class of closed or open composite structures. This paper focuses on the symmetric Envelope Interface, a special case constructed from exactly one Survey Line Spiral and one Anti-Survey Line Spiral, forming an axially symmetric closed surface. The symmetric Envelope Interface has exactly two closure points, and the radius at both closure points is exactly r0, the initial radius of the spirals. This paper further endows the symmetric Envelope Interface with a dynamic generation process: under constant angular speed omega, the generating curve first expands and then contracts, completing the generation of a complete surface within a fixed time interval. This paper presents the general definition, the specialized symmetric construction, the explicit parametric equations, the complete geometric properties, and the time evolution and dynamic generation laws of the symmetric Envelope Interface. The construction is essentially geometric; the dynamic generation is an extension of the geometric definition.