Revision History

Added Turkish translation, thanks to Süleyman Saltuk Güngör.

(legacy iOS) Changed iOS Deployment Target to iOS 14, because Apple has stopped supporting iOS 12. Thus, in particular, I no longer have a maintainable iOS 12 device to test on.

(legacy iOS) Added UINavigationBarAppearance so that navigation bars will have an opaque background when running on iOS 15.

(iOS) Changed UIRequiresFullScreen build setting from YES to NO. Once upon a time there might have been some reason that UIRequiresFullScreen was required for proper interaction with CMMotionManager, but I don't remember what the issue was, nor can I see any immediate problems with UIRequiresFullScreen = NO, other than the obvious fact that Curved Spaces looks best when it's got the full screen available. In any case, Curved Spaces will (if time permits) get replaced by a SwiftUI version (imitating the current SwiftUI version of Crystal Flight) and then later, I hope, get replaced with a VR version.

(iOS) Added Italian translation, thanks to Daniela, Isabella Eva and Davide Bigatti.

(iOS) Updated Japanese translation, thanks to Tom Sawada.

(macOS) Runs natively on both Apple Silicon and Intel Macs.

Changed various GPU uniforms, colors in buffers, etc. to half-precision (__fp16 and faux_simd_half4) where appropriate.

Removed workaround for bug that function-constant assignments like
constant bool gFoo [[ function_constant(0) ]];
constant bool gBar = ! gFoo;
used to work as expected on iOS but fail on macOS. They now work correctly on both OS’s.

(Re-)added Spanish translation, thanks to Cristian Armendariz-Picon

Added Portuguese translation, thanks to Nuno Fernandes

Replaced manual texture loading with Asset Catalogs and MTKTextureLoader.

Renders to Wide Color (Display P3) when available.

Some of the shared code that won't be needed in the upcoming SwiftUI versions of the Geometry Games apps has been migrated to "-LEGACY" files, to allow the SwiftUI versions to include desired utilities without including legacy cruft like PixelRGBA, ImageRGBA, etc.

(iOS) Converted launch screen format from .xib to .storyboard to comply with new App Store requirements.

(iOS) Toolbar self-adjusts at runtime to default height for device (iPad or iPhone).

(iOS) Made toolbar opaque to make it brighter.

Minor changes to Chinese translations of "Basic" / "Intermediate" / "Advanced".

Added spaces in support of the 3rd edition of The Shape of Space (see www.crcpress.com/The-Shape-of-Space/Weeks/p/book/9781138061217 ).

Replaced functions deprecated in iOS 13 or macOS 10.15 with non-deprecated alternatives.

(iOS) Updated for compatibility with iOS 13. In particular, it delays the presentation of the initial popover until after the base view controller has finished setting up.

(macOS) Enabled Hardened Runtime to allow Notarization by Apple.

(iOS) Added screenshots for iPad Pro (3rd Gen).

(iOS) Table images, toolbar icons and other images re-created at @1x, @2x and @3x. Source files for those images all simplified and tidied up (now mostly as iDraw files).

(iOS) Toolbar icons resized to 24pt, which is the new recommended size.

(iOS) Removed vestigial OpenGL ES code.

(iOS) Tests against an INCREMENTAL_PITCH_YAW_ROLL_THRESHOLD to avoid needlessly redrawing the scene when the scene isn't changing and the device is lying (almost) motionless on a table.

Replaced itsTilingRadius and itsDrawingRadius with itsHorizonRadius.

Culls using bounding sphere instead of polyhedron to reduce CPU load.

Tiles and culls to rigorously ensure that no "popping" can happen in the spherical and Euclidean cases. Fudges it a bit in the hyperbolic case because rigorously avoiding popping would incur too great a performance penalty (due to the exponentially increasing number of cells as a function of radius).

New: Curved Spaces for iOS

Uses tilt-to-steer interface (with thanks to Daniela Bigatti and Mark Bell for this idea)

Graphics rewritten using Metal

(macOS) On multi-GPU systems, selects the GPU that's already running the displays attached to the main computer (but ignores any externally attached removable GPUs). If the system switches to a different GPU, this app switches to that GPU as well.

(macOS) No longer calls [[NSNotificationCenter defaultCenter] removeObserver:self] because it's no longer necessary.

(macOS) Main content view is now layer-backed. When going fullscreen, avoids macOS 10.13.4 bug.

CPU code consistently uses "double" (rather than "float") for essentially everything.

(macOS) Exports images as PNG instead of TIFF.

(Mac) Mac version is now Metal-only. Reason: The Mac OpenGL version of the Geometry Games uses an older approach that would have been very time-consuming to rewrite using a CAOpenGLLayer to bring it into line with iOS OpenGL, iOS Metal and Mac Metal versions. It hardly seemed worth investing that much time into OpenGL code that would soon get phased out anyhow. In any case, users of older Macs will always be able to download an older, OpenGL-compatible version of each app.

(Mac) Given that the Mac version is now Metal-only, it now requires macOS 10.12 or later. Reason: macOS 10.12 is the only version I can test the apps on, and I prefer not to release an app for earlier versions of the operating system, on which it's never been tested.

Created a single project document with targets for iOS and macOS.

Created that single project document from scratch, to get rid of years of legacy cruft.

Modified touch interface to let rotations exactly track the mouse motion.

Added CURVED_SPACES_TOUCH_INTERFACE for immediate use on Win10 touchscreen computers, and as preparation for an iOS version as well.

(Win) Replaced GetCursorPos(), which gives the cursor position at the time of the call, with GET_X_LPARAM(lParam) and GET_Y_LPARAM(lParam), which gives the cursor position at the time of the event.

Separated OpenGL(ES)-specific data and code from graphics-system-independent data and code, in preparation for a migration from OpenGL(ES) to Metal on iOS and Mac (and maybe eventually to Vulkan on Android and to DX12 on Windows).

(Mac) Updated code for Mac OS X 10.10, replacing all deprecated method calls. Requires OpenGL 3.3.

(Mac) Converted memory management from Manual Retain-Release (MRR) to Automatic Reference Counting (ARC).

Suppressed the Language menu to avoid displaying UniHan characters incorrectly (and also because the Language menu wasn't really useful except in the Torus Games).

Added “back” buttons to Help pages' sample manifold files, and also tidied up the formatting.

Further migration to Char16.

Expanded visibility of OpenGL headers, so the ModelData can refer to OpenGL objects as GLuint instead of "unsigned int", thus improving clarity and avoiding integer conversion warnings.

Replaced L"…" → u"…" and L'·' → u'·'. The L syntax required -fshort-wchar to get 16-bit wide characters and generated copious warnings in Android, while the u syntax is part of the C11 standard.

Completed deferred maintenance of Windows version (accommodated changes from last 15 months when I had no Windows computer).

Handles localized text as UTF-16 instead of UTF-8.

(Win) Improved font quality (especially East Asian) on Windows Vista and newer.

First version requiring OpenGL 3.2 or OpenGL ES 2.0.

Last version compatible with OpenGL 2.

Public release of accumulated changes.

(Win) Moved much functionality from individual applications to shared code.

(Win) Simplified implementation of various features. Removed cruft.

Added traditional Chinese (Hant) localization, separate from simplified Chinese (Hans) localization.

(Mac) Moved much functionality from individual applications to shared code.

Replaced platform-specific language lists with a single language list in app's common code. Simplified language menu handling.

Moved endonyms and Win32 LANGIDs to Geometry Games shared code.

(Mac) Updated Objective-C syntax to use @{}, @[], @() and @autorelease.

(Mac) Re-organized instance variables, moving them from .h to .m files (@interface to @implementation) as allowed by the “new” Objective-C runtime.

(Win) To avoid bugs in Intel Integrated Graphics drivers, ignores VAO extension and directs all OpenGL 2 users (on Windows) to the legacy version of the program.

Simplified extensions handling.

Added Chinese.

Added Spanish.

Merged vertex shaders using #ifdef.

Public version offers mutually orthogonal sets of Clifford parallels.

Deeper tilings (best depth on computers from 2008 or later [i.e. OpenGL 3 era hardware]).

(Mac) imageAsBitmapImageRepOfSize rescales images larger than 1024×1024 when running with OpenGL 2 (on older computers), but leaves the requested size unchanged when running with OpenGL 3 (on mid-aged or newer computers).

(Mac) imageAsBitmapImageRepOfSize no longer rejects sizes greater than 1024×1024, but instead rescales the image.

(Win) The application as a whole is now willing to use the OpenGL 2 FBO extension for Copy/Save. However, to ensure that all users get correct basic functionality, it calls glGenerateMipmap only on OpenGL 3.3 or higher. On OpenGL 3.2 or earlier it falls back to glTexParameteri(…, GL_GENERATE_MIPMAP, …) to avoid buggy glGenerateMipmap implementations.

First version to require Vertex Array Objects.

Same as 3.4.3, but with Chinese and Spanish.

Last version to run without Vertex Array Objects (superseded by 3.4.3.1).

Disentangled Vertex Array Object (VAO) code from Vertex Buffer Object (VBO) code.

(Mac) Created an opaque ModelData typedef and move much more functionality into the GeometryGamesView class to reduce code duplication among different applications.

(Mac) Created a shared GeometryGamesView class to reduce code duplication among different applications.

(Mac) The ModelData is now packaged as an Objective-C object. The WindowController sees the ModelData and the View. The View sees the ModelData. This design goes against Apple's advice to let the Controller mediate between the Model and the View (as illustrated by the 2-way arrows in the figure at developer.apple.com/technologies/mac/cocoa.html ), but ultimately achieves much cleaner code. As an added bonus, the pointers WindowController→ModelData, WindowController→View and View→ModelData all point in a consistent direction (no cycles), so they may all be strong (retained) references. There's no longer any need for weak (non-retained) references.

(Mac) The Mac OS 10.6 style fullscreen mode would switch the first responder to the WindowController, regardless of what it had been previously. Now that Mac OS 10.7 provides a far cleaner fullscreen mode (and I've eliminated the 10.6 fullscreen mode entirely), the first responder is the View, not the WindowController. The View now handles all keystroke and mouse activity, while the WindowController handles the menus.

(Mac) Uses OpenGL 3.2 on Mac OS 10.7.

(Mac) Mac OS 10.7 fullscreen mode support.

(Mac) Assorted small changes for Mac OS 10.7 compatibility.

(Mac) Pauses animation when hidden (⌘H).

Added additional Clifford parallel options for use in talks: centerlines only; or 1, 2 or 3 mutually orthogonal sets.

Dirichlet domain wall segments use absolute dimensions for texture coordinates, not just aspect ratios.

Triangulates Dirichlet domain wall segments with 4n vertices each instead of 2n+2 vertices each. It's a fraction of a percent slower but gets the texture coordinates right even when the faces are irregular.

Lots of small improvements and maintenance, which I got bored of recording in the revision histories. Includes improvements to support older, buggier OpenGL drivers as well as newer ones.

(Mac) Rewrote user interface, replacing old single-class based architecture with simpler and more logical AppDelegate/WindowController/View architecture.

(Mac) Replaced groups of related menu command handlers with single tag-based handlers.

(Mac) Instead of using an Open File panel to select a space, uses a custom NSOutlineView. In the short run this lets the Save Image code take full advantage of Mac OS's built-in ability to return to the last directory it saved an image in. In the long run it paves the way towards an iOS version, where the file system is effectively hidden from the user.

(Mac) Simplified mouse handling.

(Win) GeometryGames-Win32-LoadEntryPoints.c loads entry points based on OpenGL version and available extensions.

Added full-screen mode (publicly available).

Added dual-projector polarized stereo 3D, for Manuel Arala Chaves at Atractor and Jouko Koskinen at Heureka. It's not part of the public version. To activate it, uncomment #define RUN_DUAL_MONITOR_FULLSCREEN_STEREO_MAC and/or #define RUN_DUAL_MONITOR_FULLSCREEN_STEREO_WIN and recompile. Selecting "Full Screen" will still give ordinary full-screen mode on a single-monitor system, but on a dual-monitor system will give dual-projector polarized stereo 3D.

Moved SetUpOneShader() to shared code, and simplified parameter handling.

Replaced application-wide texture settings (for mipmapping, anisotropic filtering, etc.) with per-texture settings. The finer control lays the foundation for iOS versions of the software, where trilinear mipmapping and anisotropic filtering are computationally more expensive.

Moved SetUpOneTexture() to shared code.

Having Copy/Save Image read the back/front buffer was a bit dicey, so Copy/Save Image now draws into an offscreen buffer instead. The new system has the flexibility to draw the image at any size, not necessarily the view size, even though there's still no user interface to set a custom size.

Extension checking moved to shared Geometry Games utilities.

New, simpler algorithm for handing window dimensions.

Eliminates ResizeGLView().

Removed and archived Preferences panel along with corresponding Help pages.

Removed and archived compile-time option for touchscreen mode, because touchscreen mode, which was written for the Mineralien- und Mathematikmuseum, was eventually incorporated into the stand-alone Kristalle software.

Show spaceship only in monoscopic 3D, to avoid "seeing the sides of our own nose". (Suppressing just the nearest image of the spaceship is dicier than you'd thing -- see discussion of "Hack A" and "Hack B" in correspondence with James Jennings.)

Uses shared GeometryGames-OpenGL.h.

Graphics code made OpenGL ES compatible.

Removed GeoWall support (could eventually get replaced with dual-projector full-screen mode if needed).

Added greyscale vs. color anaglyphic 3D.

Replaced version-based runtime choices with extension-based runtime choices.

Uses shared Geometry Games utilities.

VAO usage now controlled by extension availability instead of version number. This allows greater VAO usage, but more importantly it simplifies the code by eliminating lots of #ifdef/#else/#endif blocks.

Removed Smooth Edges from menu [and preference panel]. Multisample now gets used iff the program wants its and the host computer provides it.

(Mac) Minor changes:

• Saved NIB file as XIB file.
• XIB file declares main view as subclass of NSOpenGLView instead of subclass of NSView, which lets us set the pixel format in Interface Builder, and also affects what initializer get called.
• Removed hack from reshape method (no longer needed).
• Removed windowWillMiniaturize method (the hack it contained is no longer needed).

(Mac) Includes copy of gl3.h bundled with source code.

Added 3-sphere, projective 3-space and odd-order lens spaces.

Restricted Clifford parallels to 3-sphere. (Now that the user stay in the central copy of the fundamental domain, the Clifford parallels display consistently only in the 3-sphere. The 3-sphere is the Clifford parallels natural home.)

Spherical shader modified to shade back hemisphere correctly.

Accepts manifolds with no polyhedral Dirichlet domain, to accommodate spaces like the 3-sphere and projective 3-space.

Always draws nearest image of spaceship. (Previous hack had avoided user's left and right eyes seeing different sides of the spaceship in stereo mode, but caused flickering when user flew along a wall of the fundamental domain. Thanks to James Jennings for reporting this bug.)

Always keeps user in central copy of fundamental domain. (Previous hack had allowed display of Clifford parallels even in spherical spaces that didn't respect the particular finite set of Clifford parallels being displayed, but caused images of spaceship to mysteriously come and go. The code is cleaner now that it display only objects that live in the space itself, not in the universal cover.)

Colored spaceship's transom grey, so that when it fills the horizon in a spherical space, the user can tell that it's directed away from him/her rather than towards him/her. Thanks to James Jennings for this suggestion.

Revised graphics code OpenGL 2.0 → OpenGL 3.0. Compiles against the forward-compatible gl3.h instead of the backward-compatible gl.h.

Removed all fixed-function (OpenGL 1) graphics code.

Removed "shaders" Help page.

Far clipping plane adjusts in real-time to avoid clipping the antipodal image of the user's spaceship even when the user has chosen a field of view greater than 90°. Thanks to James Jennings for bringing this problem to my attention, as well as for various other improvements.

Moved all colors from plain (r,g,b,α) to premultiplied (αr, αg, αb, α) for correct transparency and mipmap generation.

Removed anisotropic filtering control from UI.

Replaced "anisotropic filtering" Help page with "shaders" Help page.

Reorganized texture management.

Added side-by-side stereoscopic 3D for display on polarized lens systems like GeoWall.

Revised ResizeGLView() for greater flexibility.

Fixed error in call to glDrawRangeElements() that had been causing the spinning Earth to render incorrectly.

Reorganized drawing code to use programmable vertex and fragment shaders (OpenGL 2.0) instead of old-style fixed function pipeline (OpenGL 1.5). New code uses generic vertex attributes for forward compatibility with OpenGL 3.2.

Minor user interface improvements.

Set tiling radius and drawing radius according to the SpaceType, to allow deeper tilings in flat spaces than in hyperbolic ones.

Added spaceship to mark user's position and orientation in the manifold.

(Win) Simplified loading of Open GL entry points.

(Mac) Added workaround for Mac OS 10.6 OpenGL performance issue when fog is enabled. [This issue disappared when Curved Spaces moved to programmable shaders (OpenGL 2.0), and the workaround has been removed.]

(Mac) Migrated NSString literals with UTF-8 to newer, simpler format.

Rewrote menu translation code for Mac OS 10.6 compatibility.

Moved responsibility for requesting a display redraw from platform-dependent code to platform-independent code.

Minor changes for OpenGL ES compatibility.

Minor maintenance on Win32 user interface

Reorganized drawing code to use Vertex Buffer Objects instead of display lists, because displays lists are deprecated in standard OpenGL and don't exist at all in OpenGL ES. New drawing code almost doubles the frame rate for large hyperbolic tilings (e.g. from 96fps to 186fps for the default scene) on current hardware. Note to self: glMultiDrawArrays() turned out to be a performance disaster.

Replaced OpenGL quads with generic OpenGL meshes.

Added data persistence ("user prefs" on Mac, "registry keys" on Windows) so KaleidoTile now remembers the multisampling ("Smooth Edges") setting from a previous session.

Simplified default language initialization on Mac OS X, eliminating LanguageCode.strings files.

Vertex shader avoids negative fog coordinate, which the MacBook OpenGL implementation would take the absolute value of.

Trivial tidying of code.

Cosmetic improvements to user interface.

Avoids calling ErrorMessage() when the OpenGL context is active.

Provides a clear explanation if the application gets separated from its supporting files.

Re-organized internationalization paradigm so that

• for each language, a single platform-independent file contains all localized strings and
• the Windows version no longer needs separate .rc and .dll files for each language
• (the Mac OS X version was already relieved of its language-specific NIB files at the previous revision).

Suspends continuous redraw when display is static.

Re-organized internationalization paradigm on Mac OS X, to avoid maintaining multiple copies of the NIB file.

Added Japanese, thanks to Tatsu Takeuchi.

(Win) Added Copy Image and Save Image… that work correctly with multisampling.

Minor menu reorganization.

Added technical FAQs to website.

(Mac) Modified image copying code to accommodate Mac OS 10.3.9.

(Win) Revised error messages to refer to technical FAQ.

French added, thanks to Roland Lehoucq.

For consistency with the Torus Games, double-click as well as single-click works to exit navigational mode.

Documentation upgraded to HTML 4.0.1.

Discontinued Win95 version.

Fixed bug: Avoids calling glDisable() for unsupported features. Thanks to Paul Chavez for helping track this down.

MacOS X version added.

Extensive internal re-organization to isolate platform-independent code from UI.

Help Book written.

Spinning Earth (as in Curved Spaces 1) added, with level-of-detail rendering.

Texturing respects aspect ratio to avoid "texture creep".

Faster tiling algorithm: replaced O(n²) algorithm with O(n log n) algorithm.

Faster rendering algorithm: 2-3 times faster.

Smoother rendering algorithm: cells added and removed on a frame-by-frame basis.

More flexible fog algorithm: automatically adapts to depth of tiling.

Uses programmable vertex shader to move fog computation from CPU to GPU.

Walls of fundamental cell may be fully closed, fully open or anywhere in between.

Vertex figures displayed upon demand.

Clifford parallels displayed upon demand (in spherical spaces).

Original Curved Spaces 1.0 release.