task07

Task07: Dynamic Mass-spring System using Variational Euler Time Integration

Deadline: June 19 (Thu) at 15:00pm

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Before Doing Assignment

If you have not installed Unity & Blender on your computer, install them if they are not installed on your computer.

First, update your local repository.

$ cd pba-<username>  # go to the local repository
$ git checkout main  # set main branch as the current branch
$ git branch -a       # make sure you are in the main branch
$ git fetch origin main  # download the main branch from the remote repository
$ git reset --hard origin/main # reset the local main branch same as remote repository

If you encounter some errors, give up updating your local repository and restart from the remote repository. In other words, clone the remote repository in a new location (see task00 for cloning).

Create the task07 branch and set it as the current branch.

$ git branch task07    # create task07 branch
$ git checkout task07  # switch into the task07 branch
$ git branch -a        # make sure you are in the task07 branch

Now you are ready to go!

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Problem 1

Do the following procedure (mostly similar to task06).

Create Project

• In the UnityHub, make a new Unity project named task07 under pba-<username>/task07.
• You will see project related folders like pba-<username>/task07/task07/Assets.

Create Plane

• Add a 3D plane by left click menu in the Hiearchy window (top-left), 3D Object > Plane.
• Make sure the position of the plane at (0., 0., 0.)
• Keep the other parameters default (e.g., scale is (1., 1., 1.))

Set Camera

• Set the position of the Main Camera to (0.0, 0.8, -1.8).
• Keep the other parameters default (Field of View is 60).
• Set the window resolution to 300x300.

Import Mesh

• Import the pba-<username>/task07/annulus.obj to the asset by dragging it into the Assets window (bottom).
• Click annulus prefab in the Assets window. You will see inspector window on the right. In the Model tab, enable Read/Write checkbox.
• Import the annulus Prefab to the scene by dragging annulus in the Assets window (bottom) to the Hierarchy window (top-left).
• In the Hierarchywindow, click default GameObject under the annulus prefab.
• Set the position of the annulus to (0.0, 1.3, 0.0). Make sure annulus > default's position is (0., 0., 0.).

Set Material to the Mesh

You do not see the annulus objet in the Game window (center) because default material do not show the back side of the faces. Let's fix it by creating new material.

• Make a new material by selecting the right click menu in the Assets window (bottom) Create > Rendering > Material.
• Click the New Material in the Asssets window (bottom) to show Inspectorwindow (right)
• Set the material color red by click the Base Map and set the RGB color as (255,0,0).
• Click the Render Face pull down manu in Surface Options and select Both
• Drag the New Material to the annulus > default in the Hiearchy window (left).

Add Collider

• Add a sphere collider component to the GameObject, annulus > default, by clicking "Add Component" in the inspector window of the annulus > default GameObject.
• Set the radius of the sphere collider to 0.31

Attach the Codes

• Drag following CSharp codes to the Assets window.
  • pba-<username>/task07/MyCloth.cs
  • pba-<username>/task07/TopologyOfUniformMesh.cs
  • pba-<username>/task07/BlockSparseMatrix.cs
  • pba-<username>/task07/ObjExporterToAssets.cs
• Attach MyCloth.cs in the Assets window to the default GameObject in the annulus Prefab.

This program means to compute dynamic animation of a skirt as a mass-spring system. The program uses the variational Euler's method to compute implicit time integration. The variational problem is solved using the Newton's method.

The current code does not compute the hessian of the elastic energy of the spring very accurately so the simulation is unstable. write code to correctly compute hessian of a spring.　node2vtx[i_node] stands for spring's end positions. When the return hessian can be written as float3x3[3][3] w, w[i_node][j_node] stands for Jacobian of energy gradient for i_node's position w.r.t j_node's position.

Write a few lines of code around line #140 in the pba-<username>/task07/task07/MyCloth.cs to compute hessian accurately.

Take a screenshot

• Make sure the window resolution to 300x300.
• Set up the Recorder package for screenshot video (see the Lecture Material about Unity)
• Capture the screen from 0th to 300th frame.
• Rename the screenshot image and place it as pba-<username>/task07/problem1.gif

Write down the energy value at the 300th frame shown in the Debug output in the Console window

energy at 300th frame
???

Problem 2: Blender rendering

In the previous step, you animate a mesh of cloth. Play the Unity project for more than the 500th frame, then you will see pba-<username>/tas07/task07/Assets/MyCloth.obj. Let's visualize the mesh nicely using Blender.

Launch Blender

• Launch Blender.
• You will see a default cube in the 3D viewport window. Remove it by x key or right click menu Delete.
• Save the project somewhere outside the repository.
• See the image below for the name of the windows in Blender.

Model Import

• In Blender, import the pba-<username>/tas07/task07/Assets/MyCloth.obj by selecting the menu File > Import > Wavefront (.obj).
• Make sure the MyCloth.obj is successfully imported and shown in the 3D Viewport window.

Camera Setting

• Select Camera in the Outliner window.
• Select Object tab in the Property window.
• Set the camera transform as Location: (X:0m, Y: 5m, Z: 1m), Rotation: (X:90deg, Y: 0deg, Z: 180deg), Mode XYZ Euler, Scale: (1.0, 1.0, 1.0).
• Press F12 key to see the rendered result, making sure the MyCloth.obj is rendered around the center of the image.

Output Image Resolution Setting

• Select Output tab in the Property window.
• Set the Resolution X as 400 px, Resolution Y as 300 px.
• Press F12 key to see the rendered result.

Shader Editor

• Split the window into two. You can do this by dragging the corner of a window (see Blender how to split screen and remove split screen @ blenderrian ).
• In the right 3D Viewportwindow, press the button Editor type in the top-left corner, and select the Shader Editor.
• At the top of Shader Editor window click a dropdown menu showing Object. Change the data from Object to World. This is necessary to work with environmental textures.

Environmental Lighting

• Go to Polyhaven (https://polyhaven.com/hdris), download HDR image such as https://polyhaven.com/a/golden_gate_hills. Download with 1k image with EXR format. Save it somewhere outside the repository.
• In the Shader editor node, press Shift + A to bring up the Add menu.
• Navigate to Texture and then choose Environment Texture.
• The Environment Texture node is created, but it won't show anything unless you connect it to the shader system.
• Connect the Environment Texture node to the Background shader node by clicking and dragging the output of the Environment Texture node (the yellow dot) to the input (the green dot) of the Background shader node .
• In the Environment Texture node, click the Open button.
• Select the HDR image you saved on your computer.
• If the instruction is difficult to follow, watch The ULTIMATE GUIDE to HDRI Lighting in Blender! @ CG Essentials.

Set-up Material

• Select MyCloth in the Outliner window.
• Select Material tab in the Property window
• Select New in the Property window.
• Set Base Color as (Red: 1.0, Green: 0.0, Blue: 0.0), Metallic as 0.3, and Roughness around 0.2.

Finally, press F12 key to see the rendered result. In the Blender Render window, save the image as pba-<username>/task07/problem1.png.

The image needs to be shown below.

After Doing the Assignment

After modifying the code, push the code and submit a pull request.

Notes

• Please leave the project files under pba-<username>/task07/task07/. The .gitignore will ignore the unnecessary intermediate binaries.
• The lecture do not explain detail of Unity and C#. Find your self on the internet or using chat AI (e.g., ChatGPT).
• Do not submit multiple pull requests. Only the first pull request is graded
• Do not close the pull request by yourself. The instructor will close the pull request
• If you mistakenly merge the pull request, it's OK, but be careful not to merge next time.