浮点数在tcl中的比较

Question

当我计算点和线之间的距离时,我遇到了问题.存在浮点数计算(比较表达式)问题.由于这个原因,我无法知道$ onextensionFlag的完美价值.请看以下......我可以知道出了什么问题吗？

proc calculateDistanceToLinefrompoint {P line} {
# solution based on FAQ 1.02 on comp.graphics.algorithms
# L = sqrt( (Bx-Ax)^2 + (By-Ay)^2 )

#     (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
# s = -----------------------------
#                 L^2
# dist = |s|*L # =>
#        | (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay) |
# dist = ---------------------------------
#                       L
# (Ay-Cy)(Ay-By)-(Ax-Cx)(Bx-Ax)
# r = -----------------------------
                # L^2
# r=0      P = A
# r=1      P = B
# r<0      P is on the backward extension of AB
# r>1      P is on the forward extension of AB
# 0<=r<=1    P is interior to AB

set ret 0
set Ax [lindex $line 0 0]
set Ay [lindex $line 0 1]
set Az [lindex $line 0 2]

set Bx [lindex $line 1 0]
set By [lindex $line 1 1]
set Bz [lindex $line 1 2]

set Cx [lindex $P 0]
set Cy [lindex $P 1]
set Cz [lindex $P 2]

if {$Ax==$Bx && $Ay==$By && $Az==$Bz} {
    set ret [list [GetDistanceBetweenTwoPoints $P [lindex $line 0]] 1] 
} else {
    set L [expr {sqrt(pow($Bx-$Ax,2) + pow($By-$Ay,2) + pow($Bz-$Az,2))}]
    #puts "L=$L"
    set d_val [expr {($Ay-$Cy)*($Bx-$Ax)-($Ax-$Cx)*($By-$Ay)-($Az-$Bz)*($Az-$Cz)}]
    set n_rval [expr {$d_val / pow($L,2)}]
    set n_rval [format "%0.3f" $n_rval]

    if { 0 < $n_rval && $n_rval < 1} {
        set onextensionFlag 0;# inside clipping area
    } elseif {$n_rval == 0 || $n_rval == 1} {
        set onextensionFlag 1 ;# inside clipping area (but on point)
    } elseif { $n_rval > 1 || $n_rval < 0 } {
        set onextensionFlag 2 ;# outside clipping area
    } else {
        set onextensionFlag 3 ;# consider inside clipping area
    }

    set ret [list [expr {abs($d_val) / $L}] $onextensionFlag $n_rval]


     }
    }

Answer 1

浮点数(在所有语言中,而不仅仅是Tcl)代表大多数数字有点不精确.因此,通常不应将它们作为平等进行比较,因为这实际上不太可能.相反,您应该检查两个值是否在彼此的特定量内(该量称为epsilon并考虑到浮点计算中存在小错误).

在您的代码中,您可以这样写:

set epsilon 0.001; # Small, but non-zero
if { $epsilon < $n_rval && $n_rval < 1-$epsilon} {
    set onextensionFlag 0;# inside clipping area
} elseif {abs($n_rval) < $epsilon || abs(1-$n_rval) < $epsilon} {
    set onextensionFlag 1 ;# inside clipping area (but on point)
} elseif { $n_rval >= 1+$epsilon || $n_rval <= -$epsilon } {
    set onextensionFlag 2 ;# outside clipping area
} else {
    set onextensionFlag 3 ;# consider inside clipping area
}

基本上,考虑一个数字线,你将点数改为小间隔:

                0                1
————————————————|————————————————|————————————————

至

             0-? 0+?          1-? 1+?
———————————————(—)——————————————(—)———————————————

如何检查你所处的范围然后从那里开始.