Calculus in Virtual Reality Взлом 2.20

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Описание

Calculus in Virtual Reality (CalcVR)

Lessons about Calculus and Geometry in Virtual Reality!

We have added literal depth to calculus!
The CalcVR app uses a Google Cardboard headset to enable the user to visualize concepts in multi-variable calculus within a virtual reality setting. The user can specify their own objects for visualization as well go through lessons on the geometry and calculus of multi-variable functions and the corresponding surfaces. In addition to this, there are interactive demonstrations where the user can further explore the concepts covered in the lessons. Because these elements are rendered in a virtual the user can see the depth of these mathematical objects and the multiple facets at play in the study of these mathematics topics.
Users can use any Google Cardboard (v1.0, v2.0) or compliant viewer to work on lessons related to calculus and geometry in three dimensions. The headset should have a capacitive touch button or the user should use a Bluetooth controller
This app includes the following modules:
3D Coordinates
- Rectangular 3D Coordinates
- Cylindrical Coordinate Measurements
- Cylindrical Coordinate Graphs and Regions
- Spherical Coordinate Measurements
- Spherical Coordinate Graphs and Regions
- Geometry of Vectors in 3D Quiz
Graphs in 3D
- Coordinates and Graphs in 3D
- Fundamental Planes
- Graphs in 3D
- Cylinder Surfaces
- Lines in 3D
- Planes in 3D
- Quiz on Lines in 3D
- Quiz on Planes in 3D
- Quadric Surface Playground and Exploration
Curves and Surfaces
- Parametrizing Curves
- Parametrizing Surfaces
- Transformations of Surfaces
- Quadric Surfaces Demo
- Surface Plotting Demo (for parametric forms of surfaces)
Vector Valued Functions of 1 Variable
- Interactive Playground with user input (including dynamic vector and scalar calculations/visualizations)
- Plotting VVF
- Velocity
- Speed
- Arc Length
- Acceleration
- Unit Tangent Vector
- Unit Normal Vector
- Splitting of Acceleration
- Curvature
- The Binormal Vector
Vector Fields
- Vector Field Visualization Playground
- Plotting Vector Fields
- Divergence of a Vector Field
- Curl of a Vector Field
Multivariable Functions(Update coming in Fall 2021)
-Plotting Multivariable Functions
-Contour Plots
-Limits and Continuity
-Partial Derivatives
-Directional Derivatives
-Gradients
-Tangent Planes and Linearity
-Extrema of Multivariable Functions
-Extrema on Compact Regions
Vector Calculus
-Line Integrals of Scalar Functions
-Line Integrals of Vector Fields
-Surface Integrals (Coming Soon)
Integration (Coming Soon)

-The purpose of these materials is to introduce students to important ideas from multi-variable calculus in a virtual reality setting.
- These are not to be taken as a stand-alone set of materials, but instead are supposed to supplement student work and reading.
- We have designed these to work with either a single button interface or using a Bluetooth controller. We hope to add further functionality later, including sharks with laser beams on their head (not kidding about this, but sharks with lasers is harder than you think to implement...).
- It is very important to us that these materials are available and usable for the largest group possible. We have targeted the lowest required hardware restrictions possible. In the future we may develop more for the advanced VR sets, but Google Cardboard allows us to equitably engage the widest possible audience.

История обновлений

2.20

2022-12-07

Fixes to issues that were causing some text in questions and panels to not render. Improvements to lessons in chapters on Graphs in 3D and Multivariable Functions

2.17

2022-05-27

Numerous fixes throughout lessons and playgrounds for consistent interactions with objects. New lessons on multivariable functions and edits in lessons throughout the CalcVR app.

2.14

2021-11-03

Updates to lessons in the multivariable functions. Additionally, there are updates to the lessons on vector fields and line integrals.

2.13

2021-10-06

Update to the implicit surfaces lesson and bug fixes for other mvf lessons.

2.12

2021-09-30

Overhaul of Multivariable Functions lessons including six new lessons and interactivity to first 10 lessons in the MVF Chapter.
New lessons include information on change along planes, different interpretations of multivariable functions, total differentials, and contour plots.
Minor fixes with menus and backend bugs.

2.10

2021-07-29

Added lessons on basic graphs in 3D, updated lessons on coordinates, vector valued functions of one variable, and parameterizations.
Updated user interfaces for settings and lesson controls.

2.01

2021-01-03

Changes to infrastructure to enable more responsive development and user interactions. Lessons on coordinate systems, lines and planes, and vector-valued functions of one variable have been significantly updated and have integrated activities and features with calcvr.org.

This update also fixes issues (head tracking and sensor errors) with phones that updated to iOS 14.1.

2.00

2020-08-05

V2.00
Changes to lessons on 3D coordinates, vector valued functions of 1 variable, lines, and planes to make the lessons more interactive and adapt to the feedback we have been given on their usage. Quizzes and Activities are now done in the CalcVR app as well as on our website, https://calcvr.org. We have removed the 2D lessons from the CalcVR app in favor of activities in the content section of our website, https://calcvr.org. We have also updated several visual elements to make sure that users can more easily read text and pick out visual elements.

1.85

2020-04-25

Minor bug fixes

1.82

2020-01-07

Fixed issues with Bluetooth controller buttons not working as expected and removing extra actions performed with Bluetooth controllers.

1.81

2019-09-15

Improvements to several scenes in the vector-valued functions of 1 variable lessons and demo.

1.80

2019-08-20

V1.80

Improvements to the performance of all elements of the lessons and demos. A new tutorial scene to help users get started with the CalcVR app. Improved controller support. Addition of background elements so that users have high contrast with the mathematical figures in lessons and demos. Consistency of design elements throughout the app. For more information, go to https://calcvr.org/support-and-technical-details/versions/

1.73

2019-04-10

Improvements to Vector Field Demo and introductory audio for the Contour Demo as well as a few bug fixes
Implementation of the TimeHop feature which allows users to move forward and backward a short amount of time to listen to segments of the lessons again.

1.72

2019-02-16

Improvements to the Vector Valued Function Demo including the introduction of paths used in student explorations.

1.71

2019-01-30

This update fixes several issues in the Quadric Surfaces Demo.

1.70

2019-01-16

V1.70
This update includes:
- 17 new lessons and demos on multivariable functions, vector fields, and line integrals
- Many improvements and fixes for existing material
- A 2D opening sequence to easily set up the Bluetooth controller and selecting an initial lesson or demo

1.63

2018-07-14

Minor Fixes and improvements

1.62

2018-07-11

V1.62
This update includes:
- A demo for visualizing vector fields including the ability to move around inside the vector field.
- An upgrade in the implementation of the Bluetooth controller, including the ability to map buttons for zooming in and out of graphs
- Removing the ability to click on interactable objects by looking for a fixed amount of time
- Improvements across all lessons and demos

1.60

2018-03-14

This update includes a set of ten lessons and demos that cover the geometry and calculus of vector valued functions of one variable. These cover elements like velocity, acceleration, directions of travel and turning, curvature, and the Frenet frame. All of these elements can be explored in the demo scene where the user can select which vectors and scalar quantities to examine for the prepared examples or the user can input their own vector valued function.
This update also includes some bug fixes with menus and other objects.

1.51

2018-01-14

Two new scenes added that allow users to input their own surfaces and preview upcoming visuals. We have also added a virtual keyboard that can be used for math input in conjunction with wither the reticle or Bluetooth controllers.

1.50

2018-01-05

We have updated animations and menus to run smoother across many different types of phones. The lessons have been modified to run as well as possible on older phones.
Bluetooth controller support and screen re-centering have been added to the settings menu at the feet of the user.

1.03

2017-09-26

We have significantly reduced the size of the app and added additional labeling in lessons.

1.02

2017-09-19

We have optimized a few things in the app and added further explanation and user functionality. This includes the ability to use Bluetooth controllers to interact with objects. Any controller that your iOS device recognizes as having a joystick should work.

1.01

2017-09-01

We've added Lesson 3 and made improvements throughout the app.

1.00

2017-08-22