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"The book provides an introduction to differential geometry of curves and surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3."

"This collection of ideas and results on topics of curve and surface design is intended for research in the academic environment as well as for practical use in industrial applications. Main emphasis is on minimal energy splines and geometric spline curves, and on techniques beyond tensor product surfaces."

"Contains recent ideas and results in three areas of growing importance in curve and surface design: algebraic methods, variational surface design, and some special applications. Leading researchers from throughout the world have contributed their latest work and provided several promising solutions to open issues in surface modeling."

"This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results."

"Sebagai pasar yang berkembang pesat, PV memiliki potensi untuk memberikan nilai tambah dalam rantai pasokan jika dimanfaatkan sepenuhnya. Penelitian ini membahas tentang smiling curves untuk mengukur dan menunjukkan potensi untuk menghasilkan nilai tambah bervariasi secara signifikan di seluruh rantai nilai Solar PV. Menggunakan analisis Tabel Input-Output dari OECD, ditunjukkan bahwa ketika investasi dalam PLTS sebesar 4,68 GWp sesuai rencana bisnis PLN dalam RUPTL 2021-2030, pada skenario Business as Usual sektor hulu memberikan nilai tambah yang sangat kecil. Hal ini menunjukkan ketergantungan sektor manufaktur Modul PV pada input impor. Penelitian ini juga melihat kondisi nilai tambah yang dihasilkan apabila keseluruhan fasilitas produksi PV Modul dibuat di Indonesia, didapatkan selisih sebesar 231.29 Juta USD. Untuk masing-masing skenario, didapatkan nilai tambah pada tahap pra-produksi dalam hal ini riset dan pengembangan, hampir sama sekali tidak memberikan nilai tambah yang signifikan. Terakhir penelitian ini juga menghitung berapa banyak jumlah tenaga kerja yang diserap dari kedua skenario tersebut, berapa banyak energi yang di produksi dan emisi CO2 yang direduksi, serta rekomendasi dan strategi dalam rangka meningkatkan nilai tambah di sepanjang rantai pasok Industri Panel Surya.

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As a rapidly growing market, PV has the potential to add value to the supply chain if fully utilized. This study examines smiling curves to measure and demonstrate the potential for generating value-added significantly across the Solar PV value chain. Using the Input-Output Table analysis from the OECD, it is shown that when the investment in PLTS is 4.68 GWp according to the PLN business plan in the RUPTL 2021-2030, in the Business as Usual scenario the upstream sector provides very little value-added. This shows the dependence of the PV Module manufacturing sector on imported inputs. We also see the value-added results if the entire PV Module production facility is made in Indonesia, which gets a difference of 231.29 million USD. For each scenario, an increase in value-added at the pre-production stage, in this case research and development, was found to provide almost no significant value-added. Finally, this study also calculates how much labour is absorbed from the two scenarios, how much energy is produced and CO2e emissions reduced, as well as recommendations and strategies in order to increase value-added along the supply chain of the Solar Panel Industry."

"This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces."