Overview

In this project, I implemented a real-time simulation of a cloth using a mass and spring based system. I built data structures to discretely represent the cloth, defined and applied physical constraints on them, and applied numerical integration to simulate the way cloth moves over time. Then, I implemented collisions with other objects as well as self-collisions to prevent cloth clipping. Lastly, I made a variety of shaders to visually improve the appearance of the cloth.

Part I: Masses and springs

Here is a screenshot of the cloth wireframe of scene/pinned2.json, showing the structure of the point masses and springs.

Here are some images of the wireframe (1) without any shearing constraints, (2) with only shearing constraints, and (3) with all constraints.

Part II: Simulation via Numerical Integration

ks

Shown below are final resting views of scene/pinned2.json with different values for the spring constant ks.

A low ks produces a loose cloth (more folds at top) while a high ks produces a tight cloth (less folds at top).

density

Shown below are final resting views of scene/pinned2.json with different values for density.

A low density means less downward gravitational force on the cloth (less folds) while a high density means more gravitational force (more folds).

damping

Shown below are final resting views of scene/pinned2.json with different values for damping.

A low damping value means the cloth will behave with more spring (come to rest slower) while a high damping value means the cloth will react more sluggishly (come to rest sooner).

Here is a screenshot of scene/pinned4.json at its final resting state with default values.

Part III: Handling Collisions with Other Objects

Shown below are the final resting state of scene/sphere.json with different values of ks.

Here is a screenshot of scene/plane.json at its final resting state.

Part IV: Handling Self-Collisions

Here are some gifs of scene/selfCollisions.json with varying ks and density values.

With a higher ks value, the cloth has less ripples and has a smoother look. There are less bends and folds overall.
With a lower density value, the cloth spreads out more as it hits the plane.

Part V: Shaders

Shaders are isolated programs that run in parallel on GPU, outputting a single 4 dimensional vector representing the color at an input.
There are two basic OpenGL shader types:

• Vertex Shaders apply transforms to vertices, modify properties like position and normal vectors, and write the final vertex position to gl_Position. The per-vertex values are interpolated via barycentric coordinates across the face of the polygon.
• Fragment Shaders take in geometric attributes of fragments, created after rasterization, to compute a final color value to out_color.

Blinn-Phong Shading

explain blinn=phong here.

Here are screenshots of the individual Blinn-Phong model components.

Combing the three components results in:

Texture Mapping

Here is a screenshot of the texture mapping shader

Displacement and Bump Mapping

Bump mapping results in a visual appearance of the texture on the surface, but does not change the geometry. Displacement mapping on the other hand, changes the geometry to match the texture. Here are some screenshot of bump and displacement shaders.

Bump mapping vs displacement mapping on the cloth at -o 128 -a 128.

Bump mapping vs displacement mapping on the sphere at -o 128 -a 128.

Bump mapping vs displacement mapping on the sphere at -o 16 -a 16.

The shaders at different sphere mesh coarseness are, in my opinion, not very noticeable and different. However, I would say that the lower resolution results in a less smooth surface.

Environment-mapped Reflection

Here is a screenshot of the mirror shader.