By Patrick Cozzi

Supported with code examples and the authors’ real-world event, this e-book bargains the 1st consultant to engine layout and rendering algorithms for digital globe purposes like Google Earth and NASA international Wind. The content material can be important for normal photographs and video games, specifically planet and massive-world engines. With pragmatic suggestion all through, it really is crucial interpreting for practitioners, researchers, and hobbyists in those components, and will be used as a textual content for a distinct issues path in special effects.

Topics coated include:

- Rendering globes, planet-sized terrain, and vector data
- Multithread source management
- Out-of-core algorithms
- Shader-based renderer design

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**Extra info for 3D Engine Design for Virtual Globes**

**Example text**

Public class Ellipsoid { p u b l i c E l l i p s o i d ( Vector3D r a d i i ) { // . . _ r a d i i T o T h e F o u r t h = new Vector3D ( _radiiSquared . X ✯ _radiiSquared . X , _radiiSquared . Y ✯ _radiiSquared . Y , _radiiSquared . Z ✯ _radiiSquared . Z ) ; } p u b l i c Vector3D S c a l e T o G e o d e t i c S u r f a c e ( Vector3D p ) { d o u b l e b e t a = 1 . 0 / Math . S q r t ( ( p . X ✯ p . X ) ✯ _oneOverRadiiSquared . X + ( p . Y ✯ p . Y ) ✯ _oneOverRadiiSquared . Y + ( p . Z ✯ p .

16 2. 2 WGS84 Coordinate System Geographic coordinates are useful because they are intuitive—intuitive to humans at least. OpenGL doesn’t know what to make of them; OpenGL uses Cartesian coordinates for 3D rendering. We handle this by converting geographic coordinates to Cartesian coordinates for rendering. The Cartesian system used in this book is called the World Geodetic System 1984 (WGS84) coordinate system [118]. This coordinate system is fixed to Earth; as Earth rotates, the system also rotates, and objects defined in WGS84 remain fixed relative to Earth.

Finally, we combine the conversion for surface points with scaling along the geodetic surface normal to create a conversion for arbitrary WGS84 points. The algorithm presented here uses only two inverse trigonometric functions and converges quickly, especially for Earth’s oblate spheroid. WGS84 surface points to geographic. Given a WGS84 point (xs , ys , zs ) on the surface of an ellipsoid (a, b, c) centered at the origin, the geographic point (λ, φ) is straightforward to compute. 25 26 2. Math Foundations public class Ellipsoid { p u b l i c Vector3D G e o d e t i c S u r f a c e N o r m a l ( Vector3D p ) { Vector3D n o r m a l = p .