diff --git a/utils/collection/listings/priority_slice.go b/utils/collection/listings/priority_slice.go
index eb77058..6877b48 100644
--- a/utils/collection/listings/priority_slice.go
+++ b/utils/collection/listings/priority_slice.go
@@ -5,7 +5,7 @@ import (
 	"sort"
 )
 
-// NewPrioritySlice 创建一个优先级切片
+// NewPrioritySlice 创建一个优先级切片，优先级越低越靠前
 func NewPrioritySlice[V any](lengthAndCap ...int) *PrioritySlice[V] {
 	p := &PrioritySlice[V]{}
 	if len(lengthAndCap) > 0 {
@@ -19,7 +19,7 @@ func NewPrioritySlice[V any](lengthAndCap ...int) *PrioritySlice[V] {
 	return p
 }
 
-// PrioritySlice 是一个优先级切片
+// PrioritySlice 是一个优先级切片，优先级越低越靠前
 type PrioritySlice[V any] struct {
 	items []*priorityItem[V]
 }
diff --git a/utils/geometry/position.go b/utils/geometry/position.go
index c50caca..124fd93 100644
--- a/utils/geometry/position.go
+++ b/utils/geometry/position.go
@@ -109,6 +109,19 @@ func (slf Point[V]) Max(point Point[V]) Point[V] {
 	return NewPoint(x, y)
 }
 
+// Move 返回向特定角度移动特定距离后的新的位置，其中 angle 期待的角度范围是 -180~180
+func (slf Point[V]) Move(angle, direction V) Point[V] {
+	df := float64(direction)
+	// 将角度转换为弧度
+	radian := float64(angle) * (math.Pi / 180.0)
+
+	// 计算新的坐标
+	newX := float64(slf.GetX()) + df*math.Cos(radian)
+	newY := float64(slf.GetY()) + df*math.Sin(radian)
+
+	return NewPoint(V(newX), V(newY))
+}
+
 // Min 返回两个位置中每个维度的最小值组成的新的位置
 func (slf Point[V]) Min(point Point[V]) Point[V] {
 	x, y := slf.GetXY()
diff --git a/utils/geometry/simple_circle.go b/utils/geometry/simple_circle.go
index 9cc93a7..e3fff18 100644
--- a/utils/geometry/simple_circle.go
+++ b/utils/geometry/simple_circle.go
@@ -29,6 +29,11 @@ func (sc SimpleCircle[V]) String() string {
 	return fmt.Sprintf("SimpleCircle{centroid: %v, %v, radius: %v}", sc.centroid.GetX(), sc.centroid.GetY(), sc.radius)
 }
 
+// IsZero 反映该圆形是否为零值的无效圆形
+func (sc SimpleCircle[V]) IsZero() bool {
+	return sc.radius == V(0)
+}
+
 // Centroid 获取圆形质心位置
 func (sc SimpleCircle[V]) Centroid() Point[V] {
 	return sc.centroid
@@ -74,15 +79,18 @@ func (sc SimpleCircle[V]) Area() V {
 	return sc.radius * sc.radius
 }
 
-// Projection 获取圆形投影到另一个圆形的特定比例下的位置和半径
+// Projection 获取圆形投影到另一个圆形的特定比例下的位置和半径（同心合并）
 func (sc SimpleCircle[V]) Projection(circle SimpleCircle[V], ratio float64) SimpleCircle[V] {
 	// 计算圆心朝目标按比例移动后的位置
-	distance := float64(sc.Centroid().Distance(circle.centroid))
+	distance := sc.Centroid().Distance(circle.Centroid())
 	moveDistance := distance * ratio
-	newX := float64(sc.CentroidX()) + moveDistance*(float64(circle.CentroidX())-float64(sc.CentroidX()))/distance
-	newY := float64(sc.CentroidY()) + moveDistance*(float64(circle.CentroidY())-float64(sc.CentroidY()))/distance
+	newX := float64(circle.CentroidX()) + moveDistance*(float64(sc.CentroidX())-float64(circle.CentroidX()))/distance
+	newY := float64(circle.CentroidY()) + moveDistance*(float64(sc.CentroidY())-float64(circle.CentroidY()))/distance
 
-	return NewSimpleCircle(V(float64(sc.radius)*ratio), NewPoint(V(newX), V(newY)))
+	// 计算新的半径
+	newRadius := float64(sc.radius) + (float64(circle.radius)-float64(sc.radius))*(1-ratio)
+
+	return NewSimpleCircle(V(newRadius), NewPoint(V(newX), V(newY)))
 }
 
 // Length 获取圆的周长
diff --git a/utils/random/number.go b/utils/random/number.go
index 2a42e4a..8ad0c13 100644
--- a/utils/random/number.go
+++ b/utils/random/number.go
@@ -13,6 +13,30 @@ func Int64(min int64, max int64) int64 {
 	return min + rand.Int63n(max+1-min)
 }
 
+// Int32 返回一个介于min和max之间的的int32类型的随机数。
+func Int32(min int32, max int32) int32 {
+	if min == max {
+		return min
+	}
+	return int32(Int64(int64(min), int64(max)))
+}
+
+// Float32Range 返回一个介于min和max之间的的float32类型的随机数。
+func Float32Range(min float32, max float32) float32 {
+	if min == max {
+		return min
+	}
+	return min + rand.Float32()*(max-min)
+}
+
+// Float64Range 返回一个介于min和max之间的的float64类型的随机数。
+func Float64Range(min float64, max float64) float64 {
+	if min == max {
+		return min
+	}
+	return min + rand.Float64()*(max-min)
+}
+
 // Int 返回一个介于min和max之间的的int类型的随机数。
 func Int(min int, max int) int {
 	if min == max {
diff --git a/utils/times/format.go b/utils/times/format.go
index 7f549c7..8b1a474 100644
--- a/utils/times/format.go
+++ b/utils/times/format.go
@@ -2,6 +2,7 @@ package times
 
 import (
 	"fmt"
+	"github.com/kercylan98/minotaur/utils/generic"
 	"math"
 	"strconv"
 	"time"
@@ -60,3 +61,8 @@ func IntervalFormat(time1, time2 time.Time) string {
 	}
 	return res
 }
+
+// ToSecDuration 转换为秒级 time.Duration
+func ToSecDuration[V generic.Number](v V) time.Duration {
+	return Second * time.Duration(int64(v))
+}