The Central European Baroque church (CEBc) appears to be in endless conflict with itself: at once unified and chaotic, continuous and fragmented. Architects strived for Gesamtkunstwerk, architecture and the plastic arts merging into a symphonic whole, and Zweischaligkeit, in which contrasting tectonic systems coexist as a composite, dissolving sharply-defined boundaries. The elements eternally approach singularity: a dynamic continuum.

A look at scientific/mathematical developments of the 1600's and 1700's helps place the CEBc in context: Desargues, Newton, Leibniz and Descartes all dealt with theories of synthesis and convergence. The effect of the new mathematical ideas was on architecture was a gradual transformation of space from pure, static and isolated to composite, dynamic and interpenetrating.
Architects used geometrical methods as plan generators. Transformational operations were of utmost importance, including area, rotation, reflection, translation, and coordinate transformation. Rotation is present throughout the underlying planning geometry of St. Michaelskirche, Berg am Laim (1744). The ceiling plan of Neumann's WÀGÀrzburg Residenz Hofkirche (1733) demonstrates both rotation and reflection. Another operation, Borrominian transformation, describes the mutation of a rectilinear spatial organization into an equivalent curvilinear structure, while maintaining the starting rectilinear diagram, as in Dientzenhofer's St. Niklas in Prague (1711.) Dilatation is also present in the CEBc, as in Neumann's Church of the Holy Cross at Neresheim, where the choir/altar half of the church is narrower than its nearmirror image. A parallel may be drawn between the mathematics and the architecture of the age. Descartes' fusion of number and geometric form in his Géom&eacut;trie may be likened to the ability to fuse and merge elements of the architecture such as center and transept: both reinforce a continuity previously unknown. In Architettura civile, Guarini included a study transforming a polar coordinate system to a Cartesian system. This variation of area transformation illustrates that the space as well as the perimeter is effected.

A projective transformation is related to mapping, in which a three-dimensional form may be projected onto a two-dimensional surface. In the vaulting of the CEBc a far-reaching potential of projective geometry as a form generator may be recognized. In the CEBc, the design process and the built work can be enunciated geometrically. The buildings call upon the spectator, not to dispassionately observe, but to participate emotionally.