We present an algorithm for constructing a triangulated isosurface
with guaranteed lower bounds on triangle angles.
For isosurfaces constructed from grids of unit cubes,
triangle angles are guaranteed to be greater than 8.1 degreess
except for triangles which ``surround'' or ``encircle'' grid vertices.
The isosurface mesh is also guaranteed to be the triangulation of a manifold.
Our algorithm uses dual contouring to construct an initial mesh
of quadrilaterals
and then merges isosurface vertices close to grid facets or edges
to improve mesh quality.
It triangulates the quadrilaterals to form the triangulated surface.
Vertices in the final mesh are located on the original mesh
vertices, edges or quadrilaterals.