Overview. This assignment focuses on using numerical integration to simulate
physical systems that follow well-known rules. Our focus will be on phenomena
which are well described by Partial Differential Equations (PDEs) such as simple,
physically-based models of rope, cloth, and water.
This assignment has two parts. In the check-in assignment due next week (Oct 9),
you will need to write a basic numerical integration library. For the project (Due,
Oct 19), you will need to create a physically-based simulation.
You must work alone for part 1 (the homework check-in), but you may work with a
partner for part 2 (the simulation project) â just one project turn-in needed per pair.
Part 1: Homework Check-in [100 points]
For the homework check-in associated with Project 2, you will need to implement a
numerical integration library in Processing, some sample code will be provided to
help you get started. We have implemented Eulerian integration, RK4, and Heun’s
method for you, you will need to implement the midpoint method. You will also
need to implement a special version of both midpoint and Eulerian integration
which returns a list of all values computed in integration.
You may not use any external libraries for part 1.
Part 1 has three turn-in requirements.
1A. Complete the code
Add the integrator for the midpoint method, and the version of Euler, midpoint,
which returns a list. You will only need to turn in Integrator.pde, but you will need
to edit the dxdt() and actual() functions in GroundTruth.pde to test your method on .
1B. HW2 Integration Online Questions
First, use your library to answer several integration questions posted here:
https://canvas.umn.edu/courses/194320/quizzes/329800
These questions will ask you to integrate various functions and report how much
error you get using a specific numerical integration technique vs the ground truth.
Note, computing this answer will require you to figure out the ground truth for each
of these differential equations.
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9 10
dy/dt = cos(t)
Euler Midpoint RK4 Actual
1C. Graph of integration â«sin(t) + tcos(t)dt for various techniques Second, consider the differential equation: dx/dt = sin(t) + tcos(t)
Using the initial condition x(0) = 0, and Ît = 1, integrate to approximate the true
value from 0 to 20.
Submit an image (any common format is ok) showing a graph of the following:
-The true function
-The approximation using Eulerian integration
-The approximation using midpoint integration
-The approximation using RK4 integration
You only need to make this graph for the one function given above:
dx/dt = sin(t) + tcos(t), comparing the ground truth and the three integration methods. Here is an example on a different function. Submit a zip file with both your image and Integrator.pde to the canvas turn in. Part 2: Simulation [100 points] You will need to write a rope/cloth simulation of multiple threads interacting with their environment in a smooth and natural fashion. For additional credit, you can implement a full cloth simulation or explore continuum fluid models. Required components are indicated with a star ().
Multiple Ropes (at least 2D)* (up to 50 points).
Extend the rope implementation shown in class to support multiple independent
ropes which all hang and swing freely. The ropes need to support one-way
interaction with an obstacle (e.g., a circle) by falling naturally on the obstacle. To get
all of these points, your implementation must produce smooth, natural looking
swinging behavior. Getting this behavior will require tuning your simulation
parameters, please save time for this step.
Cloth Simulation (up to 20 points).
Extend your rope simulation to include horizontal springs that bind ropes to each
other in order to make a full cloth simulation. The cloth needs to support one-way
interaction with an obstacle (e.g., a ball) by falling naturally on the obstacle. To get
all of these points, your implementation must produce smooth, natural looking
swinging behavior. Getting this behavior will require tuning your simulation
parameters, please save time for this step. [This will also count as multiple ropes.]
Air Drag for Cloth (up to 10 points).
Include an air-drag term in your cloth simulation using the method discussed in
class. Compare the results with and without drag.
3D Implementation & Rendering (up to 20 points).
Update your ropes or cloth simulation to be in 3D. To get full points here you need
both smooth 3D motion and high-quality 3D rendering with a natural camera that
allows the user to navigate around the scene from different angles and positions.
Try to use texturing and lighting to improve the rendering.
User Interaction (up to 10 points).
These points come from user interaction direction with the simulation itself (not
from controlling the camera). To get full points, the user should have a clear,
smooth, and natural way to interact with the ropes/cloth. Discrete interactions such
as toggling some behavior on/off will only receive a couple of points. Look for
continuous interaction such as allowing the user to move an obstacle with the
mouse.
Realistic Speed (up to 10 points).
Match your simulation to a reference of your choice (e.g., hold one end of a thread
and time how long it takes the other end to drop). If your simulation moves as
quickly as real threads, youâll get full credit. Slower simulations will receive partial
credit.
Ripping/Tearing (up to 10 points).
Rip or tear the cloth/rope when the forces get too large.
Continuum Water Simulation (up to 20 points).
Using a continuum-based method, like the Shallow Water Equation, to create a 1D or
2D water simulation.
Art Contest
If you generate a pretty image (even by accident), save it to submit to the class art
contest. A pool of honorable mentions will be given 2 points, and the grand winner
gets 5 points. All winners will be chosen completely subjectively.
Part 2 Project Report & Video* (10 points).
Your submission must be in the form of webpage with:
⢠Images of your particle systems
⢠A brief description of the features of your implementation and timestamp
of where they occur in your video(s).
⢠Code you wrote
⢠List of the tools/library you used
⢠Brief write-up explaining difficulties you encountered
⢠One or more videos showcasing features of your simulation
⢠Submission for the art contest (optional)
These 10 points for the submission itself will be based on the clarity of expression of
the report, and to the degree which it quickly communicates what you tried, what
worked well, and what didnât.
Additionally, each feature you expect to get credit for must be documented in your
submission videos in a way which clearly shows the resulting behavior. If you do not
show a feature in your submission video(s) you will not receive credit for it.
Part 2 Grading Criteria
Simulations must animate well and look convincing to get full credit. Partially
implemented features will receive partial credit. Points past those needed for full
credit will count as extra credit, though at a discounted rate (see Scoring below). If
you do other things you think are cool and worth credit let me know beforehand
and be sure to document it in the report.
Use of other code and tools
Anything you are getting credit for must be code you wrote for this course. You
must write the code for the simulation yourself! External libraries may be used for
aspects that are not related to simulation (e.g., rendering, camera motion, video
capture) just be sure to document that you used these.
Partners & Groups
You are strongly encouraged to work in pairs for the project. Each pair should turn
in only one assignment. Both people will be given the same grade. You cannot repeat
the same partner from a previous project.
Project Scoring
Partial credit will be given. Scores computed as follows (points above 100 possible):
-Undergraduate: Grade is â(totalPoints * 100) [e.g., 100 points will be full credit]
-Grad students: Grade is â(totalPoints * 84) [e.g., 120 points will be full credit]
*Extra credit will only be given to assignments with at least an A- on the required
features.
Sample Solution
Development of the event of E. coli in the network As a human administrations overseer in the event of contamination, I will take all fundamental measures to speak with youngsters, guardians and clinical staff in a convenient and successful manner take. My first concern is to separate illnesses however much as could reasonably be expected and to permit those effectively contaminated to get the treatment they need (Graham-Clay, 2005). On the off chance that illnesses, for example, Escherichia coli happen in a neighborhood secondary school, we will promptly illuminate the clinical staff. Escherichia coli contaminations from food cause genuine ailment, which can prompt genuine sickness and now and then demise. Since treatment is restricted, counteraction by overseeing food handling is essential to control the event of these ailments. Be that as it may, E. coli is profoundly flexible, versatile, can convey and move DNA, makes new strains and is impervious to current handling and control techniques. Further examination is required around there before full oversight is acquired. Intestinal hemorrhagic E. coli is a perceived infection because of the event of an industrially accessible inexpensive food burger. Manifestations of bacterial disease by E. coli incorporate serious looseness of the bowels, typically blood, stomach torment and spewing. Kids younger than 4 are bound to build up this illness. Related nourishments incorporate uncooked meat, unsterilized milk, juice. Defiled water can be brought about by fecal pollution of individuals who have microorganisms. Indeed, even disinfectants utilized in certain items will most likely be unable to adequately obliterate microbes. Hence, it is suggested that individuals with inabilities in the resistant framework and other high-hazard bunches abstain from eating sprouts. Chloride-treated fledglings are still connected with the improvement of E. coli and Salmonella (Taormina and Beuchat 1999). Treatment incorporates strong consideration and observing of renal capacity (CDC, 2001). As a rule, antibodies are contraindicated. The outcome of kidney disappointment might be deathThere are seven fundamental components in relational correspondence. These components exist at whatever point we connect here and there. The substance of these components is that they are firmly related and progress in an intermittent cycle. It is one. DeVito says that there are consistently wellsprings of data when two individuals convey. The originator is the wellspring of the message and is liable for encoding the message and offering importance to the message (DeVito, 2013). The beneficiary of the message being gotten by the cove is the beneficiary. Relational correspondence is a significant part of life. Notwithstanding trading data among individuals engaged with the correspondence cycle, there are other significant parts of correspondence between individuals (West, 2011). Cooperation of relational relationship assists individuals with gaining thoughts and relational abilities through the correspondence cycle (DeVito, 2009). All the more significantly, when utilizing relational correspondence, the gatherings associated with the correspondence cycle are bound to communicate their feelings and feelings. Thusly, the use of innovation during the time spent relational correspondence is still significant and assumes a significant part in the public eye (Wood, 2010). As per a study of April 2012, in the previous 30 days, about 70% of cell phone clients and 86% of cell phone clients are directing in any event one of the accompanying exercises. Subject 9 Interpersonal relationship ï¬ What is relational correspondence? Relational correspondence ï· Interpersonal correspondence is the way toward conveying, imparting, and haggling between the two individuals. Relational correspondence ï¬ What is the hypothetical perspective about relational correspondence? Relational correspondence in the 1960’s ï¬ Learning, disagreement, balance, social judgment, response. â Speech and social impact relational relationship From the last part of the 1960s to the mid 1970s â Self articulation, self divulgence, relational connections, nonverbal correspondence and relationship advancement. â Development of relational connections and relational connections Interpersonal correspondence during the 1970s MRSA contamination was initially restricted to emergency clinics and extraordinary nursing home, particularly individuals who are feeble in the invulnerable framework. Since the 1980s, network type cases and plagues have likewise been accounted for. The cases got in the network are cases not identified with hospitalization or dialysis, medical procedure or catheterization in the previous year. These contaminations typically happen in other solid individuals and are probably going to be restricted to skin diseases. Nonetheless, over the previous decade, the expanded pathogenicity of MRSA microbes has brought about more genuine, some of the time destructive network diseases. As of late, MRSA has been found in consumable creatures, and a few flare-ups are “food prompted” or foodborne. In one such episode, contaminated individuals created common side effects of foodborne infections, for example, regurgitating and stomach cramps.>
Development of the event of E. coli in the network As a human administrations overseer in the event of contamination, I will take all fundamental measures to speak with youngsters, guardians and clinical staff in a convenient and successful manner take. My first concern is to separate illnesses however much as could reasonably be expected and to permit those effectively contaminated to get the treatment they need (Graham-Clay, 2005). On the off chance that illnesses, for example, Escherichia coli happen in a neighborhood secondary school, we will promptly illuminate the clinical staff. Escherichia coli contaminations from food cause genuine ailment, which can prompt genuine sickness and now and then demise. Since treatment is restricted, counteraction by overseeing food handling is essential to control the event of these ailments. Be that as it may, E. coli is profoundly flexible, versatile, can convey and move DNA, makes new strains and is impervious to current handling and control techniques. Further examination is required around there before full oversight is acquired. Intestinal hemorrhagic E. coli is a perceived infection because of the event of an industrially accessible inexpensive food burger. Manifestations of bacterial disease by E. coli incorporate serious looseness of the bowels, typically blood, stomach torment and spewing. Kids younger than 4 are bound to build up this illness. Related nourishments incorporate uncooked meat, unsterilized milk, juice. Defiled water can be brought about by fecal pollution of individuals who have microorganisms. Indeed, even disinfectants utilized in certain items will most likely be unable to adequately obliterate microbes. Hence, it is suggested that individuals with inabilities in the resistant framework and other high-hazard bunches abstain from eating sprouts. Chloride-treated fledglings are still connected with the improvement of E. coli and Salmonella (Taormina and Beuchat 1999). Treatment incorporates strong consideration and observing of renal capacity (CDC, 2001). As a rule, antibodies are contraindicated. The outcome of kidney disappointment might be deathThere are seven fundamental components in relational correspondence. These components exist at whatever point we connect here and there. The substance of these components is that they are firmly related and progress in an intermittent cycle. It is one. DeVito says that there are consistently wellsprings of data when two individuals convey. The originator is the wellspring of the message and is liable for encoding the message and offering importance to the message (DeVito, 2013). The beneficiary of the message being gotten by the cove is the beneficiary. Relational correspondence is a significant part of life. Notwithstanding trading data among individuals engaged with the correspondence cycle, there are other significant parts of correspondence between individuals (West, 2011). Cooperation of relational relationship assists individuals with gaining thoughts and relational abilities through the correspondence cycle (DeVito, 2009). All the more significantly, when utilizing relational correspondence, the gatherings associated with the correspondence cycle are bound to communicate their feelings and feelings. Thusly, the use of innovation during the time spent relational correspondence is still significant and assumes a significant part in the public eye (Wood, 2010). As per a study of April 2012, in the previous 30 days, about 70% of cell phone clients and 86% of cell phone clients are directing in any event one of the accompanying exercises. Subject 9 Interpersonal relationship ï¬ What is relational correspondence? Relational correspondence ï· Interpersonal correspondence is the way toward conveying, imparting, and haggling between the two individuals. Relational correspondence ï¬ What is the hypothetical perspective about relational correspondence? Relational correspondence in the 1960’s ï¬ Learning, disagreement, balance, social judgment, response. â Speech and social impact relational relationship From the last part of the 1960s to the mid 1970s â Self articulation, self divulgence, relational connections, nonverbal correspondence and relationship advancement. â Development of relational connections and relational connections Interpersonal correspondence during the 1970s MRSA contamination was initially restricted to emergency clinics and extraordinary nursing home, particularly individuals who are feeble in the invulnerable framework. Since the 1980s, network type cases and plagues have likewise been accounted for. The cases got in the network are cases not identified with hospitalization or dialysis, medical procedure or catheterization in the previous year. These contaminations typically happen in other solid individuals and are probably going to be restricted to skin diseases. Nonetheless, over the previous decade, the expanded pathogenicity of MRSA microbes has brought about more genuine, some of the time destructive network diseases. As of late, MRSA has been found in consumable creatures, and a few flare-ups are “food prompted” or foodborne. In one such episode, contaminated individuals created common side effects of foodborne infections, for example, regurgitating and stomach cramps.>
