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3.Relief Maps
A third way to represent a scalar field is to fix one of the dimensions,and then plot the value of the function as a height versus the remaining spatial coordinates,say xand y,that is,as a relief map.Figure 1.2.6 shows such a map for the same function I(,xy,0) .
Figure 1.2.6 A relief map of the scalar field given by Eq.(1.2.3).
1.3 Vector Fields
A vector is a quantity which has both a magnitude and a direction in space.Vectors are used to describe physical quantities such as velocity,momentum,acceleration and force,associated with an object.However,when we try to describe a system which consists of a large number of objects (e.g.,moving water,snow,rain,…) we need to assign a vector to each individual object.
As an example,let’s consider falling snowflakes,as shown in Figure 1.3.1.As snow falls,each snowflake moves in a specific direction.The motion of the snowflakes can be analyzed by taking a series of photographs.At any instant in time,we can assign,to each snowflake,a velocity vector which characterizes its movement.
3.Relief Maps
A third way to represent a scalar field is to fix one of the dimensions,and then plot the value of the function as a height versus the remaining spatial coordinates,say xand y,that is,as a relief map.Figure 1.2.6 shows such a map for the same function I(,xy,0) .
Figure 1.2.6 A relief map of the scalar field given by Eq.(1.2.3).
1.3 Vector Fields
A vector is a quantity which has both a magnitude and a direction in space.Vectors are used to describe physical quantities such as velocity,momentum,acceleration and force,associated with an object.However,when we try to describe a system which consists of a large number of objects (e.g.,moving water,snow,rain,…) we need to assign a vector to each individual object.
As an example,let’s consider falling snowflakes,as shown in Figure 1.3.1.As snow falls,each snowflake moves in a specific direction.The motion of the snowflakes can be analyzed by taking a series of photographs.At any instant in time,we can assign,to each snowflake,a velocity vector which characterizes its movement.
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