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From Wikipedia

Isometric projection

Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angles between any two of them are 120 degrees.

Overview

The term "isometric" comes from the Greek for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection).

An isometric view of an object can be obtained by choosing the viewing direction in a way that the angles between the projection of the x, y, and zaxes are all the same, or 120°. For example when taking a cube, this is done by first looking straight towards one face. Next the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately ±35.264° (precisely arctan(sin 45°) ) about the horizontal axis. Note that with the cube (see image) the perimeter of the 2D drawing is a perfect regular hexagon: all the black lines are of equal length and all the cube's faces are the same area.

In a similar way an isometric view can be obtained for example in a 3D scene editor. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated downwards around the horizontal axes by about 35.264° as above, and then rotated ±45° around the vertical axes.

Another way in which isometric projection can be visualized is by considering a view within a cubical room starting in an upper corner and looking towards the opposite, lower corner. The x-axis extends diagonally down and right, the y-axis extends diagonally down and left, and the z-axis is straight up. Depth is also shown by height on the image. Lines drawn along the axes are at 120° to one another.

The term "isometric" is often mistakenly used to refer to axonometric projections in general. (There are three types of axonometric projections: isometric, dimetric and trimetric.)

Mathematics

There are eight different orientations to obtain an isometric view, depending into which octant the viewer looks. The isometric transform from a point a_{x,y,z} in 3D space to a point b_{x,y} in 2D space looking into the first octant can be written mathematically with rotation matrices as:

\begin{bmatrix} \mathbf{c}_x \\ \mathbf{c}_y \\ \mathbf{c}_z \\ \end{bmatrix}=\begin{bmatrix} 1 & 0 & 0 \\ 0 & {\cos\alpha} & {\sin\alpha} \\ 0 & { - \sin\alpha} & {\cos\alpha} \\ \end{bmatrix}\begin{bmatrix} {\cos\beta } & 0 & { - \sin\beta } \\ 0 & 1 & 0 \\ {\sin\beta } & 0 & {\cos\beta } \\ \end{bmatrix}\begin{bmatrix} \mathbf{a}_x \\ \mathbf{a}_y \\ \mathbf{a}_z \\ \end{bmatrix}=\frac{1}{\sqrt{6}}\begin{bmatrix} \sqrt{3} & 0 & -\sqrt{3} \\ 1 & 2 & 1 \\ \sqrt{2} & -\sqrt{2} & \sqrt{2} \\ \end{bmatrix}\begin{bmatrix} \mathbf{a}_x \\ \mathbf{a}_y \\ \mathbf{a}_z \\ \end{bmatrix}

where \alpha = \arcsin(\tan30^\circ)\approx35.264^\circ and \beta = 45^\circ. As explained above, this is a rotation around the vertical (here y) axis by \beta, followed by a rotation around the horizontal (here x) axis by \alpha. This is then followed by an orthographic projection to the x-y plane:

\begin{bmatrix} \mathbf{b}_x \\ \mathbf{b}_y \\ 0 \\ \end{bmatrix}= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}\begin{bmatrix} \mathbf{c}_x \\ \mathbf{c}_y \\ \mathbf{c}_z \\ \end{bmatrix}

The other seven possibilities are obtained by either rotating to the opposite sides or not, and then inverting the view direction or not.

History and limitations

First formalized by Professor William Farish (1759–1837), the concept of an isometric had existed in a rough empirical form for centuries. From the middle of the 19th century isometry became an "invaluable tool for engineers, and soon thereafter axonometry and isometry were incorporated in the curriculum of architectural training courses in Europe and the U.S." According to Jan Krikke (2000) however, "axonometry originated in China. Its function in Chinese art was similar to linear perspective in European art. Axonometry, and the pictorial grammar that goes with it, has taken on a new significance with the advent of visual computing".

As with all types of parallel projection, objects drawn with isometric projection do not appear larger or smaller as they extend closer to or away from the viewer. While advantageous for architectural drawings where measurements need to be taken directly, the result is a perceived distortion, as unlike perspective projection, it is not how our eyes or photography normally work. It also can easily result in situations where depth and altitude are difficult to gauge, as is shown in the illustration to the right.


Gesture drawing

A Gesture drawing is work of art defined by rapid execution. Typical situations involve an artist drawing a series of poses taken by a model in a short amount of time, often a little as 30 seconds, or as long as 2 minutes. Gesture drawing is often performed as a warm-up for a life drawing session.

In less typical cases the artist may be observing people or animals going about normal activities with no special effort to pause for the artist. For example, drawing from people on the street, performers, athletes, or drawing animals at the zoo.

More generally, a gesture drawing may be any drawing which attempts to capture action or movement.

Purpose

The primary purpose of gesture drawing is to facilitate the study of the human figure in motion. This exploration of action is helpful for the artist to better understand the exertions of muscles, the effects of twisting on the body, and the natural range of motion in the joints.

The practice allows an artist to draw strenuous or spontaneous poses that cannot be held by the model long enough for an elaborate study, and reinforces the importance of movement, action, and direction, which can be overlooked during a long drawing. Thus, an approach is encouraged which notes basic lines of rhythm within the figure. The rapidity of execution suggests an aesthetic which is most concerned with the essence of the pose, and an economy of means in its representation, rather than a careful study of modeling of light on the form.

For some artists, there is a calisthenic logic: just as an athletewarms up before exercising or participating in sports, artists use gesture drawing to prepare themselves mentally and physically for a figure drawing session. The fast pace of gesture poses help an artist "loosen up" to avoid a stiff drawing style.

The artist who undertakes gesture drawing also receives the benefits of self-training their drawing ability. This kind of very rapid drawing of the figure builds (through the act of frequent repetition) an instinctive understanding of human proportions which may aid the artist when executing more extended works.

For some artists, a gesture drawing is the first step in preparing a more sustained work. Other artists, who seek to capture brief moments of time in a direct manner, consider the gesture drawing to be the end product.

Drawing from life is often preferred over photographic reference as it allows the artist to view the model from multiple angles and without distortion of the lens or lighting. As well, the repetition of short drawings without pausing forces the artist to work intuitively.

Drawings longer than 2 minutes are usually not considered gestures, as they inevitability allow the artist more time to measure and plan the drawing, or to begin to define the form with modeling. Once the artist begins measuring, erasing, shading or otherwise improving the drawing with a second pass, they have ceased to gesture draw and begun rendering. They will be improving the complexity of their current drawing, but they are no longer practicing their ability to draw correctly in from an instant impression.



From Yahoo Answers

Question:I have a Math exam tomorrow and I suck at 3D Isometric things. So I wanna find some shapes online and try to draw them out on Isometric Paper. I cant seem to find ANYTHING! I dont want the like prisms and everything to draw, just like boxes, stacked boxes and stuff. Help me find a website that has that, Please!

Answers:{ Try these links. } http://www.inet2inet.com/Main/MainCenter.asp http://drawlogic.com/2007/09/22/as3-3d-world-engine-alternativagame/ http://en.wikipedia.org/wiki/Isometric_projection http://mathforum.org/workshops/sum98/participants/sanders/IsomExamples.html http://www.lhup.edu/~dsimanek/3D/illus1.htm http://blog.pekpongpaet.com/2009/03/09/autodesk-launches-project-dragonfly-web-based-2d3d-home-floor-planning/ http://www.nma-fallout.com/fallout3/fo3-vault1.jpg

Question:The cylinder must stick out from the right side of the isometric cube. Cube is 8 units (obviously in length, width, and height) and the length of the cylinder can be any size, just as long as the diameter is 6 units long. I am sketching this on isometric graph paper. If anyone could explain to me how to draw this or show me a tutorial on that type of sketch, it would be appreciated. My design teacher assigned this for homework but he did not explain it well. Thanx!

Answers:Check out this site it explains the procedure fully

Question:I have an assignment to create packaging for an energy efficient light globe / bulb. Drawn it as a line drawing - how do i make it 3d? Going to use yellow and black on the packaging.

Answers:Is it the package you want to make 3d or the light bulb? For the bulb select the line of the glass and use the 3d option under Effects to rotate it which should produce the bulb, the metallic bit is more tricky it depends how accurate you need it to be. For a simple box you need to draw up each of the six faces and save them as .eps files you can then, using the 3d effect create a plain white box with the dimensions you need, for example for a box 100mm wide by 150mm tall draw a box of those dimensions, guessing that it should be 100mm deep, select your box and extrude it by 100mm choosing perspective and angle of view from the defaults or create a custom view, you can then attach the eps files to it by selecting the appropriate face and apply as map art. An alternative for the box is to draw up three sides, front, top and side and position them as though the box had been flattened, by applying skew and scale to the top and side you can produce an isometric projection, if the top had a -60 skew and 80% vertical scale the side will need a +60 skew and 80% horizontal scale both these effects need to be applied from the corner where the three faces meet it would keep things simple for you if the three faces were on different layers. There is a demonstration of the 3d on this link http://www.adobe.com/designcenter/video_workshop/?id=vid0053

Question:Yeah, I know I probably sound stupid lmao, but I'm auditioning for Frank Sinatra & for a portfolio they want drawings with examples of line, others w/ examples of color, and others w/ example of value. What exactly is this O.o? I have an idea, but it's better to be safe than sorry. & Could you please provide examples/ links? Thank you. ;D i'm auditioning for fine arts

Answers:design, elements of drawing line, value, color , + shape , space, texture, form http://www.johnlovett.com/test.htm http://www.princetonol.com/groups/iad/Files/elements.htm http://www.drawinghowtodraw.com/drawing-lessons/art-design-principles/art-values-composition.html Line is basically drawing with lines only, or use of lines, cubism , Picasso, http://pablo-picasso.paintings.name/ Value is the tone or hue of color white > to gray> to black , shades, highlites Munsell-color-chart http://www.jaimetreadwell.com/Dccc-Munsell-color-chart-system.htm Color is basic colouring of items with primary, secondary, and other colors http://designelementsandprinciples.com/color2-4.htm ______ Frank Sinatra School of the Arts http://schools.nyc.gov/SchoolPortals/30/Q501/default.htm ..

From Youtube

06 Isometric drawing :CBSE Mathematics, Class VII, Chapter 15 Visualising Solid Shapes This video discusses about the concept of isometric drawing with examples. Isometric drawing is a method used to create the illusion of 3-dimensional ojbect on a plane 2-dimensional surface.

Artoonix - Isometric drawing for young people :When I was a teacher of primary age pupils, one activity that went down well every year (and which generated huge amounts of fascinating VOLUNTARY homework) was the use of isometric paper to create pseudo 3D shapes, designs and lettering. I've been doing a few experiments for an Artoonix project I would like to try, and this type of image was one that seemed like it could solve a problem. I made this little movie simply as a demo for anyone who hasn't ever tried using isometric paper. (You can find examples on the internet simply by running an image search. You can find paper like the one I used as well as dots and other variations).