Map range: Difference between revisions
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("in succession" is an unnecessary constraint. Also, it's good to encourage exposition of additional language features related to solving the problem.) |
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:<math>t = b1 + {(s - a1)(b2 - b1) \over (a2 - a1)}</math> |
:<math>t = b1 + {(s - a1)(b2 - b1) \over (a2 - a1)}</math> |
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The task is to write a function/subroutine/... that takes two ranges and a real number and returns the mapping of the real number from the first to the second range. Use this function to map the values of the integers 0 to 10 from the range [0, 10] to the range [-1, 0] |
The task is to write a function/subroutine/... that takes two ranges and a real number and returns the mapping of the real number from the first to the second range. Use this function to map the values of the integers 0 to 10 from the range [0, 10] to the range [-1, 0]. |
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'''Extra credit:''' Show additional idiomatic ways of performing the mapping, using tools available to the language. |
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Revision as of 22:19, 25 November 2010
Given two ranges:
- Range of all real numbers satisfying .
- And range of all real numbers satisfying .
Then a value s in range a is linearly mapped to a value t in range b where:
The task is to write a function/subroutine/... that takes two ranges and a real number and returns the mapping of the real number from the first to the second range. Use this function to map the values of the integers 0 to 10 from the range [0, 10] to the range [-1, 0].
Extra credit: Show additional idiomatic ways of performing the mapping, using tools available to the language.
C++
This example defines a template function to handle the mapping, using two std::pair objects to define the source and destination ranges. It returns the provided value mapped into the target range.
It's not written efficiently; certainly, there can be fewer explicit temporary variables. The use of the template offers a choice in types for precision and accuracy considerations, though one area for improvement might be to allow a different type for intermediate calculations.
<lang cpp>#include <iostream>
- include <utility>
template<typename tVal> tVal map_value(std::pair<tVal,tVal> a, std::pair<tVal, tVal> b, tVal inVal) {
tVal inValNorm = inVal - a.first; tVal aUpperNorm = a.second - a.first; tVal normPosition = inValNorm / aUpperNorm;
tVal bUpperNorm = b.second - b.first; tVal bValNorm = normPosition * bUpperNorm; tVal outVal = b.first + bValNorm;
return outVal;
}
int main() {
std::pair<float,float> a(0,10), b(-1,0);
for(float value = 0.0; 10.0 >= value; ++value) std::cout << "map_value(" << value << ") = " << map_value(a, b, value) << std::endl;
return 0;
}</lang>
Output:
map_value(0) = -1 map_value(1) = -0.9 map_value(2) = -0.8 map_value(3) = -0.7 map_value(4) = -0.6 map_value(5) = -0.5 map_value(6) = -0.4 map_value(7) = -0.3 map_value(8) = -0.2 map_value(9) = -0.1 map_value(10) = 0
PureBasic
<lang PureBasic>Structure RR
a.f b.f
EndStructure
Procedure.f MapRange(*a.RR, *b.RR, s)
Protected.f a1, a2, b1, b2 a1=*a\a: a2=*a\b b1=*b\a: b2=*b\b ProcedureReturn b1 + ((s - a1) * (b2 - b1) / (a2 - a1))
EndProcedure
- - Test the function
If OpenConsole()
Define.RR Range1, Range2 Range1\a=0: Range1\b=10 Range2\a=-1:Range2\b=0 ; For i=0 To 10 PrintN(RSet(Str(i),2)+" maps to "+StrF(MapRange(@Range1, @Range2, i),1)) Next
EndIf</lang>
0 maps to -1.0 1 maps to -0.9 2 maps to -0.8 3 maps to -0.7 4 maps to -0.6 5 maps to -0.5 6 maps to -0.4 7 maps to -0.3 8 maps to -0.2 9 maps to -0.1 10 maps to 0.0
Python
<lang python>>>> def maprange( a, b, s): (a1, a2), (b1, b2) = a, b return b1 + ((s - a1) * (b2 - b1) / (a2 - a1))
>>> for s in range(11): print("%2g maps to %g" % (s, maprange( (0, 10), (-1, 0), s)))
0 maps to -1 1 maps to -0.9 2 maps to -0.8 3 maps to -0.7 4 maps to -0.6 5 maps to -0.5 6 maps to -0.4 7 maps to -0.3 8 maps to -0.2 9 maps to -0.1
10 maps to 0</lang>