Question

我需要帮助创建一个函数来将三个角度（以度为单位，偏航俯仰和滚动）转换为六个浮点变量。

我如何将函数输出这些浮点数？

{0,0,0} = {1,0,0，-0，-0,1}
{45,0,0} = {0.70710676908493,0.70710676908493,0，-0，-0,1}
{0,90,0} = {-4.3711388286738e-08,0,1，-1,0，-4.3711388286738e-08}
{0,0,135} = {1，-0,0，-0，-0.70710676908493，-0.70710676908493}
{180,180,0} = {1，-8.7422776573476e-08,8.7422776573476e-08,8.7422776573476e-08,0，-1}
{225,0,225} = {-0.70710682868958,0.5,0.5，-0,0.70710670948029，-0.70710682868958}
{270,270,270} = {1.4220277639103e-16，-2.3849761277006e-08,1,1,1.11924880638503e-08,1.42202776319103e-16}
{315,315,315} = {0.5，-0.85355341434479,0.14644680917263,0.70710688829422,0.5,0.5}

更多示例：Egor Skriptunoff

{10,20,30} = {0.92541658878326，-0.018028322607279,0.37852230668068，-0.34202012419701，-0.46984630823135，0.81379765272141}
{10,30,20} = {0.85286849737167，-0.0052361427806318,0.52209949493408，-0.5，-0.29619812965393,0.81379765272141}
{20,10,30} = {0.92541658878326,0.21461015939713,0.3123245537281，-0.17364817857742，-0.49240386486053,0.85286849737167}
{20,30,10} = {0.81379765272141,0.25523611903191,0.52209949493408，-0.5，-0.15038372576237,0.85286849737167}
{30,10,20} = {0.85286849737167,0.41841205954552,0.3123245537281，-0.17364817857742，-0.33682405948639,0.92541658878326}
{30,20,10} = {0.81379765272141,0.4409696161747,0.37852230668068，-0.34202012419701，-0.16317591071129,0.92541658878326}

我目前拥有的代码可以计算除第2和第3之外的所有浮点数。

function convert_rotations(Yaw, Pitch, Roll)
    return {
        math.cos(math.rad(Yaw))*math.cos(math.rad(Pitch)),
        0,
        0,
        math.sin(math.rad(Pitch))*-1,
        math.sin(math.rad(Roll))*math.cos(math.rad(Pitch))*-1,
        math.cos(math.rad(Roll))*math.cos(math.rad(Pitch))
    }
end

当第二个浮点数和第三个浮点数的所有角度都非零时，我似乎无法找到正确的数学运算，但我确实想到了这个：

-- The second float when the Yaw is 0 degrees
math.sin(math.rad(Pitch))*math.sin(math.rad(Roll))*-1

-- The second float when the Pitch is 0 degrees
math.sin(math.rad(Yaw))*math.cos(math.rad(Roll))

-- The second float when the Roll is 0 degrees
math.sin(math.rad(Yaw))*math.sin(math.rad(Pitch))

对于第三次漂浮我想出了这个：

-- The third float when Yaw is 0 degrees
math.sin(math.rad(Pitch))*math.cos(math.rad(Roll))

-- The third float when Pitch is 0 degrees
math.sin(math.rad(Yaw))*math.sin(math.rad(Roll))

-- The third float when Roll is 0 degrees
math.cos(math.rad(Yaw))*math.sin(math.rad(Pitch))

Answer 1

local function Rotate(X, Y, alpha)
    local c, s = math.cos(math.rad(alpha)), math.sin(math.rad(alpha))
    local t1, t2, t3 = X[1]*s, X[2]*s, X[3]*s
    X[1], X[2], X[3] = X[1]*c+Y[1]*s, X[2]*c+Y[2]*s, X[3]*c+Y[3]*s
    Y[1], Y[2], Y[3] = Y[1]*c-t1, Y[2]*c-t2, Y[3]*c-t3
end

local function convert_rotations(Yaw, Pitch, Roll)
    local F, L, T = {1,0,0}, {0,1,0}, {0,0,1}
    Rotate(F, L, Yaw)
    Rotate(F, T, Pitch)
    Rotate(T, L, Roll)
    return {F[1], -L[1], -T[1], -F[3], L[3], T[3]}
end

偏航，俯仰和滚转旋转到六个浮点变量

1 个答案: