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Excel is a spreadsheet application that can render data calculated using 2D charts. The term 2D graph I mean the coordinate system x, y. Visualization of spatial data coordinates x, y, z using a 3D graph does not allow even the latest version (written in 2016). What Excel is presented as a 3D graph is actually only a small cosmetic changes when the data are not shown on the y-axis through moniker but as block certain height, which currently corresponds to the value y. Still, however, this is a graph of x, y (Really 2D).

3D graphs could be used some other software, but it is not easy to link calculations from Excel with some external program. Often it is a problem that I'm not that computer administrator, so you can not install additional programs. On the other hand, Excel is now standard on every computer and even smartphone. In addition to work with Excel can handle any average user. Data visualization in coordinates x, y, z can be done using two simple formulas. This method works well in any other spreadsheet that plots a graph x, y. Even in the old Excel from 1987.

What you draw is not a 3D object. It's just a set of lines in a plane substantially only an optical illusion, which reminds us of the 3D cube. To make this a credible illusion, we must follow when drawing according to certain rules. Those we explained in the previous paragraph. To explain this computer, we need rules to describe mathematically. Display (projection) of 3D objects on a 2D plane describes axonometry.

Consider a 3D right-handed coordinate system. In it are placed in 3D space points. Each point in the space of coordinates . The 3D space, however, we want to display a 2D computer screen. Like the 3D object casts a shadow on a 2D plane. The image below is a 2D plane of the projection on the screen representation of the coordinates x 'and y'. Us focus on a point P which is reflected from the 3D space to 2D plane x ', y'. Cut down its projection of a 2D x-axis' a particular value of p 1 we know that you calculate using the cosine angle. Similarly, we know calculate the other values P 1, P 2, Q 1, Q 2, r 2nd These numerical values are called coefficients of projection. This could be likened to the fact that when we change the angle of incidence of light and changes the method of projection onto the plane, changing the shape of the shadow.

Therefore necessary to specify points in 3D space to the 2D plane of the screen. To serve the general perspective projection transformation equation:

The axis is identical with the axis y, so that the ratio r 1 neglect because r 1 = 0th Coefficients projection need not be calculated manually, because in practice, the most commonly used display already calculated and expressed as the chart values:

We choose, for example, the most widely used type of display called left oblique. Dosadímekonkrétne coefficients in transformation equations. Some expressions in parentheses are multiplied by zero or units, so we get the simplified form:

For example, we want to draw dimensional wireframe cube size pages 3 and we want to view it in an oblique view. We start by describe all vertices by coordinates .

For illustration, I called the coordinates of each color. We create three columns in which they will coordinate points x, y, z describing the position of a point in 3D space. Then, we create two more columns that will be represented in 2D projection of x 'and y'. The first line of columns x 'and y' using the fill patterns for the simplified transformation equations for the x, y, populated with the values of the cells of the first three columns. Coated with the formula to be converted to the full range. Now you just portray the calculated values of the columns x 'and y' using 2D x, y graph. Renders the projection of 3D points to a 2D plane of the screen. The advantage of this solution is that if you change something in 3D coordinates, using the transformation equations are converted 2D projection that is automatically displayed in real time. For better understanding you can download directly sample file kocka.xls .

For a perfect display it needs to have both axis of the graph to scale and that the square area of the graph. Otherwise the image will be flattened. Axis plot the x 'and y' do not need to see and so they can be later removed from the chart, or hide. To draw a line must enter the start and end points. We skip the line and list the points of the other line segments. After selecting the line graph, the segment that will create a projection cubes. Image below is a preview of the file sample kocka-ciary.xls .

In another example, we draw the block size with the sides a, b, c. The procedure is similar, but do not enter the coordinates into the columns of x, y, z by hand, but the size ratio of the parallelepiped refer to the shaded cells, which are numerical values of a, b, c. The values of a, b and c can vary, but for convenience I added a dial. Click the arrow up or down to increase or decrease the value in the cell above the dial. These values are populated with up to 3D coordinates, where after transformation into a 2D projection immediately displayed as rendered block.

For Spice up I added even calculate that diverts the vertical edges of the block certain angle. One internal angle block then it is not genuine, but slightly smaller. This will provide monoclinic prism. With the cosine of an angle of deflection, and the calculated new coordinates x, y, z and deployment of new peaks in the area of the prism. You can download the sample file kvader.xls , changing values and track changes.

For a more detailed description of a tutorial can watch a video in which the step by step added to the process illustrated input of coordinates, the downstream projection of the plane x ', y', and the end coordinate calculation according to the ratio of the variable block sizes.

In the following example, I added another column called t. Basically, it's the angle in radians, which is populated with a parametric equation in a cylindrical helix. Parametric equations determine the coordinates x, y, z according to the parameter t. It is a movement along a circular path, and with each revolution (one revolution is 6.28 radians) increases the value of the coordinates to a constant, which is called pitch. Constants can rewrite and use absolute addressing, this constant populated with in each calculation. Thus, we obtain a spatial curve that resembles a spiral.

In another example, I created a trio of different projections: general axonometric, side and plan. For each type of projection is the corresponding coefficients are transformed into the coordinates x 'and y'. Of the three columns I had to portray three graphs that show exactly these three views. Coefficients of projection in this example are dosadené to fixed formulas.

Spice up the formula I has modified the parameter to be changed at each revolution not only the height (pitch) but also the distance from the center. This curve wound is not cylindrical, but conical (cone) surface. The coefficient of taper using sliders and change the value using absolute addressing transferred to the calculation, 3D coordinates. Each change of spatial coordinates after transformation in real time is displayed in three views. This will provide an object that looks like a conical spring. If you do not know exactly how to adjust the general transformation equations for different views, you can download the sample Sobor for this example: pruzina.xls and put all the custom values in column x, y, z.

The example on the 3D coordinates are translated into various predefined 2D views using five coefficients projection (taken from the table). In another example, we will show how to make a projection of a view in any arbitrary angle of rotation α, β, γ about axes x, y, z . Now we coefficients projection. considered to be constant, but their numerical values will be recalculated according to the angles α, β, γ . Since the axis ofin 3D space it is not the same as x ' of the 2D space, then neither r1 is not equal to zero, but to another account. And since it is non-zero, we can not neglect. Now therefore we consider it to five, but six of transformation coefficients p 1 , p 2 , q 1 , q 2 , y 1 , y 2 , given by the following formulas:

As an example, I created a 3D object pyramid With a footprint the size of 2 and a height of 2, with the center of the base is the same as the center of the 3D coordinate system as the base, and is divided in half 2/2 = 1st

Steering angles α, β, γ is populated with formulas to screening coefficients. Excel must be replaced angles in radians. Since the whole circle has 360 degrees which corresponds to 6.28 radians, then 1 radian is 6.28 / 360 = 0.0174 ° .

Coefficients calculated projection using absolute addressing populated with transformation equations in the general screening. By varying the angles by using the slider therefore it changes the direction of view from which we look at the 3D object. To illustrate zi Reach sample file: 3D-rotation-ihlan.xls

But it is not rotation in the literal sense, because 3D coordinates do not change, change only the angle of projection on a 2D plane. Rotation of the body in space describe the transformation matrix for rotation. These, however, in this case we do not need, thus considerably simplifying calculations.

A detailed description is in the video below, in which, step by step the process explained by their coordinates, the conversion coefficients of projection according to the angle of the projection onto the plane x ', y'.

This screening method I used in the display and GPS coordinates. I left a few hours to enable GPS in one place, so I got around 20,000 points in space. The image below is their spatial representation, the tare as cloud points. It is seen that the position determination is always to within a few meters of the center value. More on the evaluation of this experiment can read a separate article on GPS accuracy .

Answer

DIRECTOR TODD Field has only been the man behind the camera for three feature films, but he has damn well made them count. Field had a successful career as a character actor—in movies like the box office smash Twister and Stanley Kubrick's Eyes Wide Shut—before pivoting to producing/writing/directing with 2001's In The Bedroom, his feature debut that was nominated for five Oscars including Best Picture. His second film, Little Children—based on the novel of the same name by Tom Perrotta—earned another three Oscar nominations. And then we didn't see anything from Field on the big screen for more than a decade.

Tár, Field's third feature, hit theaters 16 years after the release of Little Children, and picked up right where the filmmaker left off, earning six Academy Award nominations (and, in our opinion, could have earned a couple more). The movie is centered on a powerhouse performance from Cate Blanchett, where the two-time Academy Award winner plays the fictional classical music conductor Lydia Tár, an acclaimed international figure of high culture. The movie keeps a tight focus on Lydia as both her hubris and her past catch up to her, leading the world she's built for herself to crumble around her.

Field detailed in a New Yorker profile that the 16-year gap between movies wasn't by design; through the years he was writing projects of the various projects that came up and went unfinished. This included an original script that both Leonardo DiCaprio and Christian Bale passed on and adaptations of the books The Creed of Violence, Blood Meridian, and Beautiful Ruins, and even a project about U.S. military deserter Bowe Bergdahl.

Eventually, though, Field remembered a meeting that he had with Blanchett over a decade ago; he was so inspired by the meeting that he always wanted to make sure he was able to draw something from it. This resulted in Tár being conceived and written specifically for Blanchett. “I wouldn’t have made the film without Cate,” Field told the L.A. Times. “I wrote Tár for her because of this very rich conversation she and I had 10-plus years ago about a project we wanted to do together that Joan Didion and I had written. The project never happened but the echo from that conversation was lasting and loud. Cate has a tremendous capacity for looking at narrative outside of her work as a performer and she’s truly one of the great minds of our age. Who better to play a genius, than a genius?”

Tár proved to be fruitful for all parties, as one of the best and most intellectually-challenging movies released in 2022; it currently has a 91% from critics on Rotten Tomatoes.

The movie is nominated for six Academy Awards, including Best Picture, Best Actress for Blanchett, Best Director and Best Original Screenplay for Field, as well as Best Cinematography and Best Editing. Whether the movie wins, at this point, is beside the point; audiences will be thinking about Tár long after the 95th Academy Awards on March 12.

Here's how you can see Tár for yourself.

Anyone eager to see the special collaboration between Todd Field and Cate Blanchett in Tár has a few options. First and foremost, the movie is streaming exclusively on Peacock. So if you subscribe, or already subscribe, you can check it out on there.

Stream Tár on Peacock

If you don't subscribe to Peacock, or don't want to, you can also rent or buy Tár on Prime Video or anywhere else you like to rent movies online.

Buy or rent Tár on Prime Video

If you loved Tár, you may have a good time checking out some of Todd Field's other work; as a director, he only has two other movies: In The Bedroom and Little Children, both of which are similarly intense to Tár.

Stream In The Bedroom Here

Stream Little Children Here

You can also check out some of Field's best acting work, as he made it a point in that part of his career to work with top-notch directors like Nicole Holfocener (in Walking and Talking) and Stanley Kubrick (in Eyes Wide Shut).

Stream Walking and Talking Here

Stream Eyes Wide Shut Here

There's also the Cate Blanchett of it all. She's already won two Oscars—for The Aviator and Blue Jasmine—and she probably should have won for Carol too. Plus, let's toss Ocean's 8 in, because she's just having so much fun in that one.

Stream The Aviator Here

Stream Blue Jasmine Here

Stream Carol Here

Stream Ocean's 8 Here

Then, finally, there's the aspect of Tár that largely sticks with one main character—a high-wire performance—as the world crumbles around them. For this, we recommend Uncut Gems, Shiva Baby, and A Serious Man. Thank us later.

Stream Uncut Gems Here

Stream Shiva Baby Here

Stream A Serious Man Here