仅用角度（非弧度整数运算）实现Minecraft对象绕轨需求

Got it, let's work through this orbital motion problem for Minecraft—those constraints are tricky but totally solvable with some fixed-point math and angle wrapping! Here's how I'd approach it, tailored exactly to your limitations:

Since we can't use floats/doubles and all values get rounded to integers, we'll use fixed-point scaling (multiplying all decimals by a large factor like 1000 to store them as integers) and keep our angles clamped to the -180° to 180° range required by your sin/cos functions.

Step 1: Define Your Orbital Parameters (As Scaled Integers) #

First, set up all your orbital values as scaled integers (I'll use a scale factor of 1000 here, matching your 0.017 → 17 example):

• #radius_scaled: Your desired orbit radius multiplied by 1000 (e.g., 5.2 blocks → 5200)
• #angle: Current orbit angle (starts at 0, updates each tick)
• #angle_step: How much to increment the angle each tick (e.g., 1 for 1° per tick, or 2 for 2° if you want a faster orbit)
• #full_circle: Pre-set to 360 (for angle wrapping)
• #scale_factor: Pre-set to 1000 (to reverse our scaling later)

You can set these up using Minecraft's scoreboard system:

# Initialize parameters
scoreboard objectives add orbital_vars dummy
scoreboard players set #radius_scaled orbital_vars 5200
scoreboard players set #angle orbital_vars 0
scoreboard players set #angle_step orbital_vars 1
scoreboard players set #full_circle orbital_vars 360
scoreboard players set #scale_factor orbital_vars 1000

Step 2: Wrap Angles to Stay Within -180° to 180° #

Every time you update your angle, you need to make sure it never goes outside the valid range for your sin/cos functions. Here's how to clamp it:

# Update the angle each tick
scoreboard players add #angle orbital_vars #angle_step

# Wrap angles over 180° down to negative values
execute if score #angle orbital_vars matches 181.. run scoreboard players operation #angle orbital_vars -= #full_circle orbital_vars

# Wrap angles under -180° up to positive values
execute if score #angle orbital_vars matches ..-181 run scoreboard players operation #angle orbital_vars += #full_circle orbital_vars

Step 3: Calculate Orbital Offsets (Fixed-Point Math) #

Now use sin/cos to calculate your X/Z/Y offsets. Since your sin/cos returns scaled integers (e.g., sin(90°) = 1 → 1000), multiply by your scaled radius, then divide by the scale factor to get the final integer offset:

# Get scaled sin/cos values for the current angle
execute store result score #sin_val orbital_vars run math sin(#angle)
execute store result score #cos_val orbital_vars run math cos(#angle)

# Calculate X and Z offsets (for a Y-axis orbit—adjust axes for other planes)
scoreboard players operation #dx orbital_vars = #sin_val orbital_vars * #radius_scaled orbital_vars
scoreboard players operation #dx orbital_vars /= #scale_factor orbital_vars

scoreboard players operation #dz orbital_vars = #cos_val orbital_vars * #radius_scaled orbital_vars
scoreboard players operation #dz orbital_vars /= #scale_factor orbital_vars

Step 4: Apply the Offset to Your Orbiting Object #

Finally, grab the center object's coordinates (scaled to integers), add your offsets, and set the orbiting object's position:

# Get center object's scaled coordinates (multiply by 1000 to keep precision)
execute as @e[type=armor_stand,tag=center] store result score #center_x orbital_vars run data get entity @s Pos[0] 1000
execute as @e[type=armor_stand,tag=center] store result score #center_y orbital_vars run data get entity @s Pos[1] 1000
execute as @e[type=armor_stand,tag=center] store result score #center_z orbital_vars run data get entity @s Pos[2] 1000

# Calculate target coordinates for the orbiter
scoreboard players operation #target_x orbital_vars = #center_x orbital_vars + #dx orbital_vars
scoreboard players operation #target_y orbital_vars = #center_y orbital_vars  # Keep Y same, or add a scaled offset here
scoreboard players operation #target_z orbital_vars = #center_z orbital_vars + #dz orbital_vars

# Set the orbiter's position (divide by 1000 to convert back to Minecraft's coordinate system)
execute as @e[type=armor_stand,tag=orbiter] store result entity @s Pos[0] double 0.001 run scoreboard players get #target_x orbital_vars
execute as @e[type=armor_stand,tag=orbiter] store result entity @s Pos[1] double 0.001 run scoreboard players get #target_y orbital_vars
execute as @e[type=armor_stand,tag=orbiter] store result entity @s Pos[2] double 0.001 run scoreboard players get #target_z orbital_vars

Quick Optimizations & Adjustments #

• Slower/Faster Orbits: If you want a slower orbit (e.g., 0.5° per tick), scale your angle by 2—store #angle as actual angle * 2, increment by 1 each tick, then divide by 2 before passing to sin/cos.
• Different Orbital Planes: To orbit around X or Z instead of Y, swap which axis uses sin/cos (e.g., for X-axis orbits, use sin for Y offset and cos for Z offset).
• Higher Precision: If 1000x scaling isn't enough, use 10000x—just make sure your scoreboard values don't overflow (Minecraft supports integers up to ~2 billion, so 10000x is safe for most orbit sizes).

内容的提问来源于stack exchange，提问作者James