Pino Trogu
Drawing a milk carton and a plastic bottle.
updated
Download these files if you want to try the drawing yourself:
Layout specifications for this demo (9x12 sheet but millimeter specs):
res.trogu.com/drawing/pdf/2-point_perspective_option2_millimeters_9x12_layout.pdf
Layout specifications for larger 11x17 sheet (inch specs):
res.trogu.com/drawing/pdf/2-point_perspective_option_1_inches_11x17_layout.gif
Object specifications for larger layout (in inches):
res.trogu.com/drawing/pdf/2-point_perspective_option1_3-inch_object.pdf
This second part shows the steps to actually construct the drawing: first the general cubic shape, and then the step-up and horse-shoe-shape cutout parts. Frequent visual comparisons, between the lines drawn on the flat drawing and the lines drawn on the three-dimensional physical model, help in understanding the mechanics, and the exact step-by-step construction of a perspective drawing, which is a kind of "projective geometry" drawing. This second part of the demonstration is also an updated version of the video I uploaded on Nov. 15, 2012: Two-point perspective tutorial -- youtube.com/watch?v=bj9MBwo61nU. This new version is also in high definition and has better sound. Shortly I will also post the corresponding files and drawing handouts so that you could try doing it on your own. Many thanks to Kevin Husley for making the original tutorial, on which this demo is based, available on his website: http://www.khulsey.com/.
Note: at 15:08 the step is to draw the Horizon Line, 5 cm above the Ground Line (showing through the tracing paper), but the position of the Ground Line is not given. Later, at 18:09, the ground line is also drawn on the tracing paper, but its position is again not given: it is 6.5 cm down from the Picture Plane line. For complete specifications, download the handout with all the measurements:
res.trogu.com/drawing/pdf/2-point_perspective_option2_millimeters_9x12_layout.pdf
This first part describes the setting up of the "scene" and includes a physical, three-dimensional model -- a kind of miniature stage set. The model includes a plexiglas "picture plane" onto which have been drawn projection and vanishing lines and the horizon line. The plexiglas is punctured at the corners of the object drawing, and threads connecting the "eye" of the viewer to the corners of the physical shape pass through the holes. The model demonstrates how the 2D-drawn perspective is a combination of lines drawn on the "ground plane" and lines drawn on the "picture plane". In the last part, the camera is placed exactly at the same vantage point as the observer in the model (the tip of the tube representing a person), showing that the view of the physical object behind the screen, and its drawn version on the screen coincide.
Download these files if you want to try the drawing yourself:
Layout specifications for this demo (9x12 sheet but millimeter specs):
res.trogu.com/drawing/pdf/2-point_perspective_option2_millimeters_9x12_layout.pdf
Layout specifications for larger 11x17 sheet (inch specs):
res.trogu.com/drawing/pdf/2-point_perspective_option_1_inches_11x17_layout.gif
Object specifications for larger layout (in inches):
res.trogu.com/drawing/pdf/2-point_perspective_option1_3-inch_object.pdf
This demonstration is an updated version of the video recorded on April 25, 2011: Two-point perspective tutorial -- youtube.com/watch?v=bj9MBwo61nU. This new version is also in high definition and has better sound. Many thanks to Kevin Husley for making the original tutorial, on which this demo is based, available on his website: http://www.khulsey.com/.
At 09:20 my explanation of the Dürer engraving showing the device to draw "exact" pictures should have clarified that the projection being discussed is a perspective projection: the string is pulled from different points on the object but always goes to the same nail on the wall – the vanishing point. For a more detailed, hands-on introduction, see also this other video: Drawing a milk carton and a plastic bottle:
youtu.be/pQTrzoSbJCg?t=6
And this one, which seems to be a favorite -- Isometric Basics:
youtube.com/watch?v=cnjnQ0zIZ-w
This video shows how to build the rough cube by cutting the parts from card stock paper and joining them together using scotch tape. It's only "rough" because we use scotch tape, however the parts still need to be drawn and cut exactly. To make the parts, we use the template (master cookie-cutter) drawn with the compass and the aid of the circular grid, by transferring the shape onto a new sheet using a push-pin to mark the corners of the pattern.
This video shows how to position the internal pattern of the cube section in relation to the sectioned external face of the cube. The patterns must touch either an edge or a vertex of the face section at a location that, if the pattern were rotated, would assure that each successive join is correct and matching. The part of the cube's face that is shown is also properly oriented and vertical. Tracing paper is used to test the correct configuration.
github.com/nytimes/covid-19-data
Video shows how to filter out all states but California, all CA counties but San Francisco, and also filter by date to show only data from the last day in the datasets, in this case Feb. 22, 2021.
nytimes.com/interactive/2020/us/california-coronavirus-cases.html
The NYT's chart uses per capita data. In the graph, each day is a small rectangle colored with a shade equivalent to the corresponding value in each cell. In this case shades of orange. Several steps were needed to create this dataset, also cutting/pasting from a JSON file, and this time definitely doing the "subtraction" so that each cell contains exactly the number of cases or deaths for just that one day; not the cumulative total up that day.
nytimes.com/interactive/2020/us/california-coronavirus-cases.html
The Excel version of the file I created shows the different steps (workbooks) I had to make to combine the deaths and the cases into one file. I chose "cases" first and copy/pasted that data; then I repeated this for deaths. The main trick was to align the states exactly when doing the combining into the same workbook. I made the county lines white and a few other edits. I did more editing in Illustrator, especially creating a clipping mask for the base map (see next video).
nytimes.com/interactive/2020/us/coronavirus-us-cases.html
Scroll down to the States table where the little colored strips to the right are (heat maps). Show all, then drag mouse to select all the rows and paste into Excel. It works surprisingly well, but you must clean it up and properly set the headers (videos shows this). The map was made in Tableau but relative area tends to skew the perception of the data (big states with fewer people get a lot of ink). Video shows also how to import and use a json file with similar data into Tableau.
Note: at first in the video I show the cases chart instead, but later I find the mistake by doing a spot check against the same chart on the NYT covid page. Always check your graph against the actual data.
But... it includes about 350 days times about 3000 US counties, so the file is more that a million rows! I had to combine data from other files found online instead. See iLearn assignment for details.
github.com/nytimes/covid-19-data.
The NYT main coronavirus page is:
nytimes.com/interactive/2020/us/coronavirus-us-cases.html
This video shows how to generate the bar chart (one bar for each day) and then overlap the thicker line on top of the bars. The line shows the "7-day moving average" so it's smoother and gives a better trend view of the pandemic. The bars are good to see each individual days but because these can vary by a lot, they are better than a line which would look very jagged.
Note: the NYT file includes "cumulative" data, so each day shows the total since the pandemic started; it adds the current day number to the previous total. This means that the default bar/line will be always going up. Instead, we want to display the "daily" count (how many new cases in that particular day). In Tableau I show how to do this with a "calculation" using subtraction without changing the original file. We duplicate the bars, change them to line; and this time apply two calculations, the subtraction and the 7-day average (although for some reason in the reverse order). These steps are the same for number 2, 3, and 4.
Note that the dataset included all days (about 350) times all the states, so that's almost 2000 rows, so if using current set, create a new files with the days (rows) just for the state you choose. Sort by state in Excel, the dates somehow will stay in order; keep the headers of course. In the video this graph is done only in Tableau.
github.com/nytimes/covid-19-data
The NYT main coronavirus page is:
nytimes.com/interactive/2020/us/coronavirus-us-cases.html
This video again shows how to generate the bar chart (one bar for each day) and then overlap the thicker line on top of the bars. Here we do it in Excel; the line is made by adding a "trend line" (the 7-day moving average).
github.com/nytimes/covid-19-data.
The NYT coronavirus page:
nytimes.com/interactive/2020/us/coronavirus-us-cases.html
This video shows how to generate the bar chart (one bar for each day) and then overlap the thicker line on top of the bars. The line shows the "7-day moving average" so it's smoother and gives a better trend view of the pandemic. The bars are good to see each individual day but because these can vary by a lot, they are better than a line which would look very jagged.
Note: the NYT file includes "cumulative" data, so each day shows the total since the pandemic started; it adds the current day number to the previous total. This means that the default bar/line will be always going up. Instead, we want to display the "daily" count (how many new cases in that particular day). In Tableau I show how to do this with a "calculation" without changing the original file. We duplicate the bars, change them to line; and this time apply two calculations, the subtraction and the 7-day average (although for some reason in the reverse order). These steps are the same for number 2, 3, and 4 videos.
Update 2021-08-22: added timestamps below for a few corrections related to recent changes in the class structure and assignments.
Note: if watching on computer, watch video at high resolution (HD up to 1440) as your connection will allow.
8:10 The discussion about buying a different set of tools for more complex or simpler drawings does not apply anymore starting in Fall 2021. See link below for list of required tools (the compass is required.)
11:27 There is no optional wooden letter drawing this semester, but you are welcome to watch video in the playlist and sketch the letters on your own.
12:39 The compass is again required starting with the Fall 2021 semester.
13:15 The clothespin technical drawings, orthographic and isometric, with tools, are actually optional starting in Fall 2021. These are different from the required clothespin/tape dispenser/lightbulb freehand drawing.
15:02 The 2-point perspective tutorial (the horseshoe shape) is actually the same for everyone.
15:27 The last color perspective drawing is required.
16:49 Get 9x12 paper pads (sketching, drawing, and tracing paper) as soon as possible. Use letter size (8.5x11) in the meantime. Sketching paper provided in class starting in Spring 2022.
20:10 In Fall 2021 the class was bichronous, meeting once a week on zoom. Starting in Spring 2022, the class is hybrid, meeting once a week in-person.
The video is about my art school background and I show a catalog of projects from my high school. The video shows also some of my drawings and sketches and also drawings from a student's portfolio.
You can also download a PDF with a visual reference for each tool, a description, and links to online sources for each item. http://static.trogu.com/documents/classes/320/tools/320_tools_supplies_trogu_SPRING_2022.pdf
See also the specific video demonstrating each tool and the use of supplies:
youtube.com/watch?v=FgFqSxECFjM
00:18 Shows a small milk carton (Gold Fish carton -- packaging). Get one for upcoming drawings. The carton is approximately a cube, about 3 inches on each side including the slanted roof part. The exact Gold Fish carton size is Net Weight 2 OZ (57 g)
00:57 Quick introduction about the three types of projection: orthographic, axonometric, and perspective.
03:23 Description of orthographic projection, showing the three planes of projection, first as a 3D model, then flattened to form a single sheet.
05:00 Description of axonometric projections
06:20 Description of perspective
07:12 Start drawing cubes
07:48 Draw title block at the beginning
09:56 Writing in title block, I actually forgot to write the number; only wrote the "#" symbol. Make sure to write the drawing number. This time, drawing the border, title block, and entering the text took about 3 minutes (ends at 11:05) -- see title block assignment page for correct sequence of information in title block.
11:03 Start practicing sketching the cube on a different sheet, not the one where you just drew the title block.
15:40 Every drawing is an abstraction, even when the object being drawn is a concrete object, a naturalistic object, an everyday object, and the drawing looks natural and resembles reality.
17:45 Try different angles besides isometric (30/30).
19:00 Don't do extreme angles at first, so to avoid drawing any face as a perfect square (while showing other sides of the cube at the same time). That's an unrealistic and "incorrect" view.
20:05 The above drawing would be "impossible". That is, possible to draw, but an impossible view in real life.
23:15 The only way to see both sides, kind of straight, is to turn the cube keeping both top and bottom hidden. Shows also how one should close one eye to get a simplified view since we always otherwise see in 3D, and have two pictures of any object at the same time. Shows also bringing the front of the cube all the way up to one's nose, then seeing just one side with one eye and the opposite side with the other eye, with the middle square in beween; or, an impossible view normally. Instead of a 3D picture of a cube, we now see two distorted pictures of squares on the sides and one connecting, thin vertical rectangle in the middle. It looks like a very strange perspective.
24:57 Explanation of binocular, stereoscopic vision (seeing with 2 eyes = seeing in 3D) by placing a finger (or a pencil) a few inches in front of one's nose and then closing one eye alternatively. The image of the pencil will appear to jump from left to right and vice-versa. But in fact, we always see both at the same time and our nervous system combines the two into a "normal" image. The images formed in each retina are also upside down.
25:25 In the video I say that the image "moves" from left to right. In reality, both images are still with reference to each respective eye. What changes a lot in the two views is the relationship of the observed object (finger, pencil, etc) to objects in the background, which changes dramatically and makes the object in front appear to "jump" instead.
26:10 Drawing and sketching cubes again.
26:28 Don't use eraser.
26:50 Keep one set of lines, the vertical, parallel to the edge of the sheet, so the cube looks like it's sitting normally on a flat, horizontal surface.
35:05 Examples of fun cubes (Scarpa's chains).
35:50 Bricard mechanism (Raoul Bricard)
en.wikipedia.org/wiki/Raoul_Bricard
00:15 Draw Parallel lines is the second assignment from Spring 2021 onward.
05:00 to 10:10 Title block again, it takes five minutes, do it first.
16:50 It's good to practice drawing lines at an angle of 30 degrees (isometric projections) as it will help with the drawing of cubes at an angle. This will help avoid views of the cube where one face looks exactly like a square.
Draw a 1/2" border around the drawing sheet and add a 3/4" title block at bottom for the drawing information to be entered: • Assignment number & title (shortened as needed) • Roster number & First and Last name • SFSU DES 320 Trogu • Drawing due date. Video shows how to draw the lines free-hand using the edge of a board as a guide (carpenter's method). Use tools, straight edge and/or drafting triangles if you already have them, otherwise use the free-hand method.
02:43 The assignment drawing # and assignment title can go into the same first block, without a vertical line separating them (see course assignment page for current sequence).
10:30 Mention of future exercise (video) which shows how to do lettering. This link goes to various lettering excercise materials: res.trogu.com/drafting/lettering/lettering.html
12:04 The date on the drawing should be the due date.
ReMAR 2018 4Th IEEE/IFToMM International Conference on Reconfigurable Mechanisms & Robots Delft University of Technology (TU Delft) 20–22 June 2018
Pino Trogu – San Francisco State University USA
Visiting Scholar, TU Delft 2017-2018
Fast Forward Session II – Lecture Room A, 15:30
Interactive Session II – Lagerhuysch, 16:30 – 18:00
Wednesday, 20 June 2018
The 6-minute film tries to capture the influence of Provinciali's teachings on my own work and teaching. In the film, look for Provinciali's initials (MP) and mine (PT) at the bottom of the screen to identify the work of the master and that of the disciple.
During the projection a text in Italian prepared by Pino Trogu (in absentia) was read aloud to the audience. You can get the text at the links below:
Italian:
bit.ly/326xbsE
or
English:
bit.ly/34Swu8d
Many thanks to: Marcella Cannalire, Antonio Cirenza, Marcello Franca, Antonio Grasselli, Deborah Sussman, Viola Tonucci
***
A note on the music: Chopin - Nocturne in C Minor, Op. 48, No. 1. Francesco Trogu, Piano. Recorded on November 30, 2012, San Francisco Conservatory of Music. The video with this soundtrack was uploaded on Sept. 17, 2020. The original video uploaded on Sept. 15, 2012 contained copyrighted music (The Köln Concert by Keith Jarrett) and has since been deleted.


