134 Pages 292 B/W Illustrations
    by A K Peters/CRC Press

    136 Pages
    by A K Peters/CRC Press

    136 Pages 292 B/W Illustrations
    by A K Peters/CRC Press

    Easily Create Origami with Curved Folds and Surfaces

    Origami—making shapes only through folding—reveals a fascinating area of geometry woven with a variety of representations. The world of origami has progressed dramatically since the advent of computer programs to perform the necessary computations for origami design.

    3D Origami Art presents the design methods underlying 3D creations derived from computation. It includes numerous photos and design drawings called crease patterns, which are available for download on the author’s website. Through the book’s clear figures and descriptions, readers can easily create geometric 3D structures out of a set of lines and curves drawn on a 2D plane.

    The author uses various shapes of sheets such as rectangles and regular polygons, instead of square paper, to create the origami. Many of the origami creations have a 3D structure composed of curved surfaces, and some of them have complicated forms. However, the background theory underlying all the creations is very simple. The author shows how different origami forms are designed from a common theory.

    Axisymmetric 3D Origami
    Four Basic Types
    Basic Crease Patterns
    Flat-Pleat Cone Type
    Flat-Pleat Cylinder Type
    3D-Pleat Cone Type
    3D-Pleat Cylinder Type
    "Twist Closing" for Closing a Solid
    Solid with Curved Surfaces
    Stabilizing a Shape

    Extension of Axisymmetric 3D Origami
    Connecting Two 3D Origami Shapes (Cylinder Type)
    Connecting Different 3D Origami Shapes (Cylinder Type)
    Connecting Different 3D Origami Shapes (Cone Type)
    Changing Pleat Orientation (Flat-Pleat Type)
    Resizing Pleats (Cylinder Type)

    Connecting Axisymmetric 3D Origami Shapes
    Connecting and Tiling 3D-Pleat Type on a Plane
    Connecting Flat-Pleat Type
    Connecting Different 3D Origami Shapes
    Making Use of Duality
    Layering Dual Patterns

    Making Use of Mirror Inversion
    Cone-Based 3D Origami
    Mirror Inversion on a Developable Surface
    Specifying Mirror Planes by a Polygonal Line
    Relation between Sweep Locus and Shape
    Various Shapes

    Application of Mirror Inversion
    Curved Fold Units Combined Together
    Inversion by Oblique Mirror Plane

    Voronoi Origami
    Tiling with Different Polygons
    Origami by Voronoi Tiling

    Various Origami Designs

    Origami Design Techniques
    Rigid Origami
    Curved Folds and Curved Origami
    Computational Origami
    Origami with Thick Materials
    Robots and Origami
    Relation between Living Things and Origami
    Origami and Mathematics
    Origami and Education
    Application of Origami to Industry



    Jun Mitani is a professor of information and systems in the Faculty of Engineering at the University of Tsukuba. Dr. Mitani was previously a PRESTO researcher at the Japan Science and Technology Agency, a lecturer in the Department of Computer Science at the University of Tsukuba, and a postdoctoral researcher at RIKEN. His research focuses on computer graphics, including computer-aided origami design techniques. He is the author of the books Spherical Origami and 3D Magic Origami.

    "This is a beautiful book, containing many lovely examples at the forefront of geometric origami. Readers will find the patterns both challenging and satisfying to fold, and the concepts on which they are based form a foundation for many further potential explorations."
    —Dr. Robert J. Lang, Origami Artist and Consultant, LangOrigami.com

    "Ever wonder how paper artists can fold a sheet of paper into amazingly complex shapes? Then this book is for you. There aren’t many resources out there for 3D, mathematically inspired origami, and Jun Mitani gives us a whole book’s worth of fun, interesting models to help fill this gap. Geometric origami fans will love this book."
    —Thomas C. Hull, Western New England University and Author of Project Origami: Activities for Exploring Mathematics, Second Edition