  The freeform architectural modeling process often involves two important
stages: concept design and digital modeling. In the first stage, architects
usually sketch the overall 3D shape and the panel layout on a physical or
digital paper briefly. In the second stage, a digital 3D model is created using
the sketch as a reference. The digital model needs to incorporate geometric
requirements for its components, such as the planarity of panels due to
consideration of construction costs, which can make the modeling process more
challenging. In this work, we present a novel sketch-based system to bridge the
concept design and digital modeling of freeform roof-like shapes represented as
planar quadrilateral (PQ) meshes. Our system allows the user to sketch the
surface boundary and contour lines under axonometric projection and supports
the sketching of occluded regions. In addition, the user can sketch feature
lines to provide directional guidance to the PQ mesh layout. Given the 2D
sketch input, we propose a deep neural network to infer in real-time the
underlying surface shape along with a dense conjugate direction field, both of
which are used to extract the final PQ mesh. To train and validate our network,
we generate a large synthetic dataset that mimics architect sketching of
freeform quadrilateral patches. The effectiveness and usability of our system
are demonstrated with quantitative and qualitative evaluation as well as user
studies.
