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Perspective projections

A perspective projection is defined by a center of projection and a plane of projection . The projector rays connect the points in the scene with the center of projection, thus highlighting thecorresponding points in the plane of projection. The [link] shows a section where the plane of projection produces a straight line whose abscissa is d , and the center of projection is in the origin.

By similarity of two triangles it is easy to realize that the point having ordinate y gets projected onto the plane in the point having ordinate y p y d z .

In general, the projection of a point having homogeneous coordinates x y z 1 onto a plane orthogonal to the z axis and intersecting such axis in position d is obtained, in homogeneous coordinates, by multiplication with the matrix 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 d 0 . The projected point becomes x y z z d , which can be normalized by multiplication of all its element by d z . As a result, we obtain x d z y d z d 1

Parallel views

Parallel views are obtained by taking the center of projection back to infinity ( ). In this way, the projector rays are all parallel.

Orthographic projection

The orthographic projection produces a class of parallel views by casting projection rays orthogonal to the planeof projection. If such plane is positioned orthogonally to the z axis and passing by the origin, the projection matrix turns out to beparticolarly simple: 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 . Among orthographic projections, the axonometric projections are based on the possibility to measure the object along three orthogonalaxes, and on the orientation of the plane of projection with respect to these axes. In particular, in the isometric projection the projections of the axes form angles of 120 ° . The isometric projection has the property that equal segments on the three axes remain equal when theyare projected onto the plane. In order to obtain the isometric projection of an object whose main axes areparallel to the coordinate axes, we can first rotate the object by 45 ° about the y axis, and then rotate by 1 2 35.264 ° about the x axis.

Oblique projection

We can talk about oblique projection every time the projector rays are oblique (non-orthogonal) to the projection plane. In order to deviate the projector rays from the normal direction by the angles θ and φ we must use a projection matrix 1 0 θ 0 0 1 φ 0 0 0 0 0 0 0 0 1

Casting shadows

As we have seen, Processing has a local illumination model, thus being impossible to cast shadows directly. However, bymanipulating the affine transformation matrices we can cast shadows onto planes. The method is called flashing in the eye , thus meaning that the optical center of the scene is moved to the point where the light source ispositioned, and then a perspective transformation is made, with a plane of projection that coincides with the planewhere we want to cast the shadow on.

The following program projects on the floor the shadow produced by a light source positioned on the y axis. The result is shown in [link]

Casting a shadow

size(200, 200, P3D); float centro = 100;float yp = 70; //floor (plane of projection) distance from center float yl = 40; //height of light (center of projection) from centertranslate(centro, centro, 0); //center the world on the cube noFill();box(yp*2); //draw of the room pushMatrix();fill(250); noStroke(); translate(0, -yl, 0); // move the virtual light bulb highersphere(4); //draw of the light bulb stroke(10);popMatrix(); pushMatrix(); //draw of the wireframe cubenoFill(); rotateY(PI/4); rotateX(PI/3);box(20); popMatrix();// SHADOW PROJECTION BY COMPOSITION // OF THREE TRANSFORMATIONS (the first one in// the code is the last one to be applied) translate(0, -yl, 0); // shift of the light source and the floor back// to their place (see the translation below) applyMatrix(1, 0, 0, 0,0, 1, 0, 0, 0, 0, 1, 0,0, 1/(yp+yl), 0, 0); // projection on the floor // moved down by yltranslate(0, yl, 0); // shift of the light source to center // and of the floor down by ylpushMatrix(); // draw of the cube that generate the shadow fill(120, 50); // by means of the above transformationsnoStroke(); rotateY(PI/4); rotateX(PI/3);box(20); popMatrix();

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Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Media processing in processing. OpenStax CNX. Nov 10, 2010 Download for free at http://cnx.org/content/col10268/1.14
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