iOS app

Rotation4D

Keizo Watanabe

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内容提要

您有没有想过观看并触摸四维物体?旋转4D 是高维可视化应用程序。它实时地渲染四维凸正多胞形(例如四维超正方体),以及三维凸正多胞形(又称柏拉图立体)。简单的触摸手势可让您直观地操作该几何图形。您还可以轻点屏幕上的按钮对多胞形添加几种特殊效果。这些效果帮助您对四维空间的理解。

单指手势

请用一个手指轻拂当前显示的多胞形,从而该多胞形在我们通常的三维空间中会旋转。轻点多胞形就停止旋转。

双指手势

请用两个手指捏合或张开,以开始在一个隐藏的空间轴和其余的轴之间旋转。此手势只对于四维多胞形是有效的。

三指手势

请用三个手指向上或向下轻扫设备屏幕,以观看同维度的其他多胞形。向左或向右轻扫在四维和三维之间切换。

“彩色/白色”按钮

此按钮可在彩光和白光之间切换。您可以选择使用哪一种来照亮多胞形。

“同步/不同步”按钮

如果此设置为“同步”,光源与多胞形的自转同步公转。

“标出/不标出”按钮

此设置为“标出”,每个多胞形的一个胞或者面就用选择的颜色标出。

“维基百科”按钮

此按钮用作超链接到关于多胞形的维基百科条目。正在非英文条目显示时会有“英文”按钮,您可以使用此按钮打开对应的英文条目。

“.png”,“.mv4”,“.mov”按钮

您可以捕捉屏幕上的图像或视频。轻点一片扩展名按钮对应的内容就保存,分享,或者发送。

“夹角”,“色相”按钮

彩色光源间的夹角每次轻点“夹角”都会变化。标出的颜色也可以以同样的方式用“色相”改变。

“目录”按钮

轻点这个按钮就可以打开目录页。

“平面,交叉,平行”开关(在目录页中)

您可以用这个开关立体观察多胞形。请选择交叉观察法或平行观察法,然后请移动您的视线融合两个图像。

兼容性

需要 iOS 11.0 或更高版本。

版本 1.33 中新功能

改进网络访问功能。

彩色正一百二十胞体的屏幕快照 立体正一百二十胞体的屏幕快照

Description

Have you ever wanted to see and touch four-dimensional objects? Rotation4D is a real-time visualization app that renders the four-dimensional convex regular polytopes such as the tesseract as well as the three-dimensional ones known as the Platonic solids. Simple touch gestures let you intuitively manipulate those geometric figures. Buttons on the screen offer some effect options that can be applied to the polytopes, which helps you understand four-dimensional space.

One-finger Gestures

Flick the polytope currently displayed with one finger and it will rotate in our usual three-dimensional space. Tapping the polytope stops rotation.

Two-finger Gestures

Pinching in and out with two fingers starts rotation between the hidden fourth spatial axis and the other axes. These gestures are only available for the 4D polytopes.

Three-finger Gestures

Swipe the screen of your device up or down with three fingers to see another polytope of the same dimensions. Swiping left and right switches between 4D and 3D.

"Color/White" Button

This button toggles between colorful and white light. You can choose which to use to illuminate the polytopes.

"Sync/Unsync" Button

When this setting is switched to "Sync", the light sources revolve in synchronization with the rotation of polytopes.

"Mark/Unmark" Button

If you switch this setting to "Mark", one of the cells or faces of each polytope will be marked in your selected color.

"Wikipedia" Button

This button provides the links to Wikipedia articles describing the polytopes. "English" button, which is revealed with a non-English article, takes you to the equivalent in English.

".png", ".mp4", ".mov" Buttons

You can capture still and moving images on the screen. Tapping each button saves, shares or sends a content with one of the file extensions.

"Angle", "Hue" Buttons

The angle between the color light sources varies every time you tap "Angle". You can also change the marking color in the same way with "Hue".

"TOC" Button

Tapping this button opens the table of contents pages.

"Flat, Cross, Parallel" Switch (in TOC pages)

This switch enables stereopsis of the polytopes. Choose cross-eyed viewing or parallel viewing, then move your eyes to merge two images.

Compatibility

Requires iOS 11.0 or later.

What's New in Version 1.33

Improved Web access.

Screenshot of Color 120-cell Screenshot of Color 120-cell