In a final, production quality rendering of a ray traced work, multiple rays are generally shot for each pixel, and traced not just to the first object of intersection, but rather, through a number of sequential ' bounces ', using the known laws of optics such as " angle of incidence equals angle of reflection " and more advanced laws that deal with refraction and surface roughness.

Their rotation in time dt is dθ, just the same angle as the rotation of the trajectory r ( t ).

Similarly, the source just below the top of the slit will interfere destructively with the source located just below the middle of the slit at the same angle.

If the Earth were perfectly spherical and homogeneous, then longitude at a point would just be the angle between a vertical north-south plane through that point and the plane of the Greenwich meridian.

Bradley explained this effect in the context of Newton's corpuscular theory of light, by showing that the aberration angle was given by simple vector addition of the Earth's orbital velocity and the velocity of the corpuscles of light, just as vertically falling raindrops strike a moving object at an angle.

* In the context of communication waveforms, the time-variant angle, or its modulo value, is referred to as instantaneous phase, often just phase.

" Optimum sail angle can be approximated by pulling the sheet in just so far as to make the luffing stop, or by using of tell-tales-small ribbons or yarn attached each side of the sail that both stream horizontally to indicate a properly trimmed sail.

It is best seen just after sunset and before sunrise in spring and autumn when the zodiac is at a steep angle to the horizon.

Tamponade is treated by pericardiocentesis, the gentle insertion of the needle of a syringe into the pericardial sac ( avoiding the heart itself ) on an angle, usually from just below the sternum, and gently withdrawing the tamponading fluids.

In this scenario, the ball is fired into a wormhole at an angle such that, if it continues along that path, it will exit the wormhole in the past at just the right angle to collide with its earlier self, thereby knocking it off course and preventing it from entering the wormhole in the first place.

In this situation, the billiard ball emerges from the future at a different angle than the one used to generate the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow.

The location of Stirling Bridge at the date of the battle is not known with certainty, but four stone piers have been found underwater just north () and at an angle to the extant 15th century bridge, along with man-made stonework on one bank in line with the piers.

When the angle between the sun and the horizon is less than 10 percent, as it is just after sunrise or just prior to sunset, sunlight becomes too red due to refraction for any colors other than those with a reddish hue to be seen.

is called conformal ( or angle-preserving ) at if it preserves oriented angles between curves through with respect to their orientation ( i. e., not just the acute angle ).

These benefits are enhanced in their levels in Chez-Maze, by giving it a challenging puzzle angle just like Sudoku.

Note that the fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that it is impossible to trisect all angles: for example, it is relatively straightforward to trisect a right angle ( that is, to construct an angle of measure 30 degrees ).

Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

The result of the observations is Af where the phase angle, Q, is measured in degrees from new moon and the probable errors include absolute as well as relative errors.

According to Philippoff, the recoverable shear S is given by Af where **yc is the angle of extinction.

Babe Ruth, as he always did in the Stadium, played right field to avoid having the sun in his eyes, and Tommy Thevenow, a rather mediocre hitter who played shortstop for the St. Louis Cardinals, knocked a ball with all his might into the sharp angle formed by the permanent stands and the wooden bleachers, where Ruth could not reach it.

where is 1 au, is the phase angle, the angle between the Sun – Body and Body – Observer lines.

On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.

For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.

where θ is the true angle SEE ′, is the apparent angle S ′ EE ′, and is the relative speed between the presumed fixed frame of reference ( such as heliocentric ) and the observer's one.

where m and n are nonnegative integers with, is the azimuthal angle in radians, and is the normalized radial distance.

where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.

Athletic jump smashes, where players jump upwards for a steeper smash angle, are a common and spectacular element of elite men's doubles play.

Asymmetry can be manifested in the size of the breast, the position of the nipple-areola complex ( NAC ), the angle of the breast, and the position of the inframammary fold, where the breast meets the chest.

where A is the radiation angle of the lamp — the full vertex angle of the emission cone.

The quantum hall effect is another example of measurements with high magnetic fields where topological properties such as Chern-Simons angle can be measured experimentally.

The tension at r is parallel to the curve at r and pulls the section to the right, so it may be written Tu =( Tcos φ, Tsin φ ), where T is the magnitude of the force and φ is the is the angle between the curve at r and the x-axis ( see tangential angle ).

To rotate a figure counterclockwise around the origin by some angle is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where

In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where

Thales ' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle.

If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

Merchant has found that the same basic relationships which describe the geometry and force systems in the case of the cutting mechanism can also be applied to the discontinuous chip formation provided the proper values of instantaneous shear angle and instantaneous chip thickness or cross-sectional area are used.

A sufficiently good approximation for determining the end reflection losses R can be obtained from the angle independent Fresnel formula: Af.

With integration, the effect of a small acceleration ( or small platform tilt angle ) can be seen after a time.

The angle between those lines can be measured, and is the angular separation between the two stars.

Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures.

The stock is hinged so the flukes can orient toward the bottom ( and on some designs may be adjusted for an optimal angle depending on the bottom type ).

Similarly, the angle that a line makes with the horizontal can be defined by the formula

6 ) at a finite distance from the axis ( or with an infinitely distant object, a point which subtends a finite angle at the system ) is, in general, even then not sharply reproduced, if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop ; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil.

3D beading generally uses the techniques of bead weaving, which can be further divided into right angle weave and peyote stitch.

* Lenses for the Canon EF mount, introduced with the company's EOS family of film SLRs in 1987 and used to this day on Canon full-frame and APS-H EOS DSLRs, can function fully on the company's APS-C DSLRs that use the EF-S mount ( although their angle of view will be different on the smaller APS-C sensor ).

The apex of the breast, which includes the nipple, can have a flat angle of projection ( 180 degrees ) or acute angle of projection ( greater than 180 degrees ).

To insure that this resultant is normal to the surface of the water, and therefore can be effectively nulled by the force of the water beneath, the normal to the surface must have the same angle, that is,

Most LCDs also have poorer color rendition and can change color with viewing angle, though modern PVA and IPS LCDs have greatly attenuated these problems.

In two dimensions the position vector which has magnitude ( length ) and directed at an angle above the x-axis can be expressed in Cartesian coordinates using the unit vectors and:

* Viewing angle is the maximum angle at which images on the monitor can be viewed, without excessive degradation to the image.

The disc remains in motion while travelling on its edge at a slight angle, and can travel exceedingly far in ideal situations.

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.