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Page "Scene graph" ¶ 25
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If and object's
If an object's reference count reaches zero, the object has become inaccessible, and can be destroyed.
* If an object's parts are entirely replaced over time, as in the Ship of Theseus example, in what way is it the same?
:::: If a container wishes to support windowless embedded objects, it needs to provide functionality to embedded objects to replace the functionality normally provided by an embedded object's window.
If radio waves strike an electrically conductive object of any size, they are slowed according to that object's permeability and permittivity.
If an object's mass does not change, the Minkowski inner product of its four-momentum and corresponding four-acceleration A < sup > μ </ sup > is zero.
If an object at equilibrium has a compressibility less than that of the surrounding fluid, the object's equilibrium is stable and it remains at rest.
If the object is much denser than the fluid, then B approaches zero and the object's upward acceleration is approximately − g, i. e. it is accelerated downward due to gravity as if the fluid were not present.
If an object's surface is in shadow, there will be more front facing shadow surfaces between it and the eye than back facing shadow surfaces.
If the object is less dense than the liquid then it will begin to sink until the weight of the displaced liquid becomes equal to the object's weight ; then it will float at that depth.
If nothing stops this crack from propagating through the material, it will cause the object's structure to fail.
If it is correct, they say " Yes " and the player sticks a flag into the object's sculpture.
# If the body is a spherically symmetric shell ( i. e. a hollow ball ), no gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
If the object is retracted out of a coil with aternating current running through it, the object's dipoles will become randomized and the object will be demagnetized.

If and bounding
If the user has magnified a document so that only part of it is visible on his computer screen, and then scrolls in it, it is useful to use a bounding box ( or in this case, a bounding rectangle scheme ) to quickly determine which scene graph elements are visible and thus actually need to be drawn.
If is a set of triangles, we can precalculate a bounding sphere.
If one chooses axis-aligned bounding boxes, one gets AABBTrees.
If the problem is to solve a Dirichlet boundary value problem, the Green's function should be chosen such that vanishes when either x or x < nowiki >'</ nowiki > is on the bounding surface. Thus only one of the two terms in the surface integral remains.
If the problem is to solve a Neumann boundary value problem, the Green's function is chosen such that its normal derivative vanishes on the bounding surface, as it would seems to be the most logical choice.
If the ductus is moderate or large, widened pulse pressure and bounding peripheral pulses are frequently present, reflecting increased left ventricular stroke volume and diastolic runoff of blood into the initially lower-resistant pulmonary vascular bed.
If the ray or viewing frustum does not intersect the bounding volume, it cannot intersect the object contained in the volume.
If non-convex bounding volumes are required, an approach is to represent them as a union of a number of convex bounding volumes.
If seen as a control system this would be encoded as a feedback error function or in a heuristically assisted system as an algorithm combined with set of heuristics bounding its operational space.
* If the current node is the bounding node for the search value then search its data array.
* If no bounding node was found then insert the value into the last node searched if it still fits into it.
If no bounding node is found then finish.
* If the bounding node does not contain the value then finish.
If a supporting hyperplane also intersects the polytope, it is called a bounding hyperplane ( since it is a supporting hyperplane, it can only intersect the polytope at the polytope's boundary ).
If threatened, they gallop away, bounding stiff-legged into the air every few strides ; a behaviour known as stotting.

If and volume
If the volume is the molal volume, then Af is obtained on a molal basis which is the customary terminology of the chemists.
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
If the retailer and hotelman's downtown unit sales have been decreasing, however, his dollar volume continues to rise, and it is dollars which you put in the bank.
If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?
* Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume.
If the boat floats, the mass of the boat ( plus contents ) as a whole divided by the volume below the waterline is equal to the density of water ( 1 kg / l ).
If weight is added to the boat, the volume below the waterline will increase to keep the weight balance equal, and so the boat sinks a little to compensate.
If the occulting object has an atmosphere, however, some of the luminosity of the star can be refracted into the volume of the umbra.
If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid.
If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.
If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter ( due to the hard-rod repulsion between the two idealized objects ).
If both sides of this equation are divided by the volume of this small piece of the charge distribution dV, the result is:
If momentum is to be conserved in a volume, changes in the momentum of matter through the Lorentz force must be balanced by changes in the momentum of the electromagnetic field and outflow of momentum.
If is the momentum of all the particles in a volume, and the particles are treated as a continuum, then Newton's second law gives
If brewers decide to convert their brew to a non-alcoholic brew they must consider the volume of liquid they have lost from the removal of the alcohol.
If the liquid is heated a little over 100 ° C, the transition from liquid to gas will occur not only at the surface, but throughout the liquid volume: the water boils.
If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.
If the field is increased past the optimum, further volume reductions are possible with minimal increase in cost.
If it is used for its relation between pressure and volume and temperature, a thermometric material must have three properties:
If a sound absorbing sheet is slid in between the prongs of a vibrating fork, reducing the waves reaching the ear from one prong, the volume heard will actually increase, due to a reduction of this cancellation.
If the liquid is incompressible the molar volume is constant and the integral becomes.
If an industry is characterized by a varying demand ( that is, a demand with cyclical fluctuations ), it is more difficult for the firms in the cartel to detect whether any change in their sales volume is due to a demand fluctuation or to cheating by another member of the cartel.

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